Comparaison système d'affichage des formules mathématiques

On compare les différents systèmes d'affichage des formules mathématiques sur les inégalités entre moyennes arithmétique, géométrique, harmonique et quadratique, sur le code LaTeX suivant.

\min_{1\le k\le n} x_k 
\le \frac{n}{\displaystyle\sum_{k=1}^n \frac{1}{x_k}} 
\le \sqrt[n]{\prod_{k=1}^n x_k} 
\le \frac{1}{n} \sum_{k=1}^n x_k 
\le \sqrt{\frac{1}{n} \sum_{k=1}^n {x_k}^2} 
\le \max_{1\le k \le n} x_k

Rendu visuel

Image PNG via texvc
MathML: $min_{1 \leq k \leq n} x_{k} \leq \frac{n}{\sum_{k = 1}^{n} \frac{1}{x_{k}}} \leq \sqrt[n]{\prod_{k = 1}^{n} x_{k}} \leq \frac{1}{n} \sum_{k = 1}^{n} x_{k} \leq \sqrt{\frac{1}{n} \sum_{k = 1}^{n} {x_{k}}^{2}} \leq max_{1 \leq k \leq n} x_{k}$
MathJax: $\displaystyle\min_{1\le k\le n} x_k \le \frac{n}{\displaystyle\sum_{k=1}^n \frac{1}{x_k}} \le \sqrt[n]{\prod_{k=1}^n x_k} \le \frac{1}{n} \sum_{k=1}^n x_k \le \sqrt{\frac{1}{n} \sum_{k=1}^n {x_k}^2} \le \max_{1\le k \le n} x_k$
KaTeX: $ 1 \leq k \leq n min x k \leq k = 1 \sum n x k 1 n \leq \sqrt [ n] k = 1 \prod n x k \leq n 1 k = 1 \sum n x k \leq ⎷     n 1 k = 1 \sum n x k 2 \leq 1 \leq k \leq n max x k $
Zwikix: min_1≤k≤n x_k ≤ n/∑_k=1ⁿ 1/x_k ≤ ⁿ√∏_k=1ⁿ x_k ≤ 1/n ∑_k=1ⁿ x_k ≤ √(1/n ∑_k=1ⁿ x_k²) ≤ max_1≤k≤n x_k

Ces différents systèmes peuvent aussi être comparés sans les fichiers CSS, en sélectionnant dans l'onglet « Affichage » du navigateur, pour le style de la page, « aucun style ». Les deux premiers systèmes ne changent pas, l'affichage par MathJax devient illisible, tandis que l'affichage par Zwikix reste lisible.

Code final

Image PNG

52 caractères

<img src='../images/comparaison-moyennes.png'>

MathML

2124 caractères

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mstyle displaystyle="true">
  <munder>
    <mo form="prefix" movablelimits="true">min</mo>
    <mrow>
      <mn>1</mn>
      <mo>≤<!-- ≤ --></mo>
      <mi>k</mi>
      <mo>≤<!-- ≤ --></mo>
      <mi>n</mi>
    </mrow>
  </munder>
  <msub>
    <mi>x</mi>
    <mi>k</mi>
  </msub>
  <mo>≤<!-- ≤ --></mo>
  <mfrac>
    <mi>n</mi>
    <mstyle displaystyle="true">
      <munderover>
        <mo>∑<!-- ∑ --></mo>
        <mrow>
          <mi>k</mi>
          <mo>=</mo>
          <mn>1</mn>
        </mrow>
        <mi>n</mi>
      </munderover>
      <mfrac>
        <mn>1</mn>
        <msub>
          <mi>x</mi>
          <mi>k</mi>
        </msub>
      </mfrac>
    </mstyle>
  </mfrac>
  <mo>≤<!-- ≤ --></mo>
  <mroot>
    <mrow>
      <munderover>
        <mo>∏<!-- ∏ --></mo>
        <mrow>
          <mi>k</mi>
          <mo>=</mo>
          <mn>1</mn>
        </mrow>
        <mi>n</mi>
      </munderover>
      <msub>
        <mi>x</mi>
        <mi>k</mi>
      </msub>
    </mrow>
    <mi>n</mi>
  </mroot>
  <mo>≤<!-- ≤ --></mo>
  <mfrac>
    <mn>1</mn>
    <mi>n</mi>
  </mfrac>
  <munderover>
    <mo>∑<!-- ∑ --></mo>
    <mrow>
      <mi>k</mi>
      <mo>=</mo>
      <mn>1</mn>
    </mrow>
    <mi>n</mi>
  </munderover>
  <msub>
    <mi>x</mi>
    <mi>k</mi>
  </msub>
  <mo>≤<!-- ≤ --></mo>
  <msqrt>
    <mfrac>
      <mn>1</mn>
      <mi>n</mi>
    </mfrac>
    <munderover>
      <mo>∑<!-- ∑ --></mo>
      <mrow>
        <mi>k</mi>
        <mo>=</mo>
        <mn>1</mn>
      </mrow>
      <mi>n</mi>
    </munderover>
    <msup>
      <mrow>
        <msub>
          <mi>x</mi>
          <mi>k</mi>
        </msub>
      </mrow>
      <mn>2</mn>
    </msup>
  </msqrt>
  <mo>≤<!-- ≤ --></mo>
  <munder>
    <mo form="prefix" movablelimits="true">max</mo>
    <mrow>
      <mn>1</mn>
      <mo>≤<!-- ≤ --></mo>
      <mi>k</mi>
      <mo>≤<!-- ≤ --></mo>
      <mi>n</mi>
    </mrow>
  </munder>
  <msub>
    <mi>x</mi>
    <mi>k</mi>
  </msub>
</mstyle>
</math>

MathJax

26732 caractères (sans compter les feuilles de style annexes)

<span class="MathJax_Preview"></span><span style="" aria-readonly="true" role="textbox" id="MathJax-Element-1-Frame" class="MathJax"><nobr><span style="width: 39.703em; display: inline-block;" id="MathJax-Span-1" class="math"><span style="display: inline-block; position: relative; width: 34.213em; height: 0px; font-size: 116%;"><span style="position: absolute; clip: rect(0.23em, 1000em, 5.377em, -0.406em); top: -2.371em; left: 0em;"><span id="MathJax-Span-2" class="mrow"><span id="MathJax-Span-3" class="mstyle"><span id="MathJax-Span-4" class="mrow"><span id="MathJax-Span-5" class="munderover"><span style="display: inline-block; position: relative; width: 2.532em; height: 0px;"><span style="position: absolute; clip: rect(1.526em, 1000em, 2.532em, -0.469em); top: -2.371em; left: 0.323em;"><span style="font-family: STIXGeneral;" id="MathJax-Span-6" class="mo">min</span><span style="display: inline-block; width: 0px; height: 2.371em;"></span></span><span style="position: absolute; clip: rect(1.564em, 1000em, 2.544em, -0.406em); top: -1.534em; left: 0em;"><span id="MathJax-Span-7" class="texatom"><span id="MathJax-Span-8" class="mrow"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-9" class="mn">1</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-10" class="mo">≤</span><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-11" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-12" class="mo">≤</span><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-13" class="mi">n</span></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="padding-left: 0.188em;" id="MathJax-Span-14" class="msubsup"><span style="display: inline-block; position: relative; width: 0.988em; height: 0px;"><span style="position: absolute; clip: rect(1.822em, 1000em, 2.597em, -0.512em); top: -2.425em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-15" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span><span style="position: absolute; top: -2.059em; left: 0.536em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-16" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-17" class="mo">≤</span><span style="padding-left: 0.313em;" id="MathJax-Span-18" class="mfrac"><span style="display: inline-block; position: relative; width: 3.111em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(1.822em, 1000em, 2.595em, -0.471em); top: -3.101em; left: 50%; margin-left: -0.296em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-19" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span><span style="position: absolute; clip: rect(2.214em, 1000em, 5.406em, -0.475em); top: -2.401em; left: 50%; margin-left: -1.495em;"><span id="MathJax-Span-20" class="mstyle"><span id="MathJax-Span-21" class="mrow"><span id="MathJax-Span-22" class="munderover"><span style="display: inline-block; position: relative; width: 1.455em; height: 0px;"><span style="position: absolute; clip: rect(2.096em, 1000em, 3.869em, -0.395em); top: -3.233em; left: 0.027em;"><span style="font-family: STIXSizeOneSym; vertical-align: -0.524em;" id="MathJax-Span-23" class="mo">∑</span><span style="display: inline-block; width: 0px; height: 3.233em;"></span></span><span style="position: absolute; clip: rect(1.564em, 1000em, 2.478em, -0.475em); top: -1.059em; left: 0em;"><span id="MathJax-Span-24" class="texatom"><span id="MathJax-Span-25" class="mrow"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-26" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-27" class="mo">=</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-28" class="mn">1</span></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span><span style="position: absolute; clip: rect(1.636em, 1000em, 2.377em, -0.475em); top: -3.409em; left: 0.512em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-29" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="padding-left: 0.188em;" id="MathJax-Span-30" class="mfrac"><span style="display: inline-block; position: relative; width: 1.108em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(1.533em, 1000em, 2.532em, -0.374em); top: -3.047em; left: 50%; margin-left: -0.296em;"><span style="font-family: STIXGeneral;" id="MathJax-Span-31" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.371em;"></span></span><span style="position: absolute; clip: rect(3.384em, 1000em, 4.306em, -0.512em); top: -3.301em; left: 50%; margin-left: -0.494em;"><span id="MathJax-Span-32" class="msubsup"><span style="display: inline-block; position: relative; width: 0.988em; height: 0px;"><span style="position: absolute; clip: rect(1.822em, 1000em, 2.597em, -0.512em); top: -2.425em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-33" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span><span style="position: absolute; top: -2.059em; left: 0.536em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-34" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; clip: rect(0.849em, 1000em, 1.239em, -0.485em); top: -1.298em; left: 0em;"><span style="border-left: 1.108em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.25px; vertical-align: 0em;"></span><span style="display: inline-block; width: 0px; height: 1.078em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; clip: rect(0.849em, 1000em, 1.239em, -0.485em); top: -1.298em; left: 0em;"><span style="border-left: 3.111em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.25px; vertical-align: 0em;"></span><span style="display: inline-block; width: 0px; height: 1.078em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-35" class="mo">≤</span><span style="padding-left: 0.313em;" id="MathJax-Span-36" class="mroot"><span style="display: inline-block; position: relative; width: 3.834em; height: 0px;"><span style="position: absolute; clip: rect(2.213em, 1000em, 5.407em, -0.448em); top: -3.987em; left: 1.125em;"><span id="MathJax-Span-37" class="mrow"><span id="MathJax-Span-38" class="munderover"><span style="display: inline-block; position: relative; width: 1.509em; height: 0px;"><span style="position: absolute; clip: rect(2.096em, 1000em, 3.87em, -0.435em); top: -3.233em; left: 0em;"><span style="font-family: STIXSizeOneSym; vertical-align: -0.524em;" id="MathJax-Span-39" class="mo">∏</span><span style="display: inline-block; width: 0px; height: 3.233em;"></span></span><span style="position: absolute; clip: rect(1.564em, 1000em, 2.478em, -0.475em); top: -1.059em; left: 0.027em;"><span id="MathJax-Span-40" class="texatom"><span id="MathJax-Span-41" class="mrow"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-42" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-43" class="mo">=</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-44" class="mn">1</span></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span><span style="position: absolute; clip: rect(1.636em, 1000em, 2.377em, -0.475em); top: -3.41em; left: 0.539em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-45" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="padding-left: 0.188em;" id="MathJax-Span-46" class="msubsup"><span style="display: inline-block; position: relative; width: 0.988em; height: 0px;"><span style="position: absolute; clip: rect(1.822em, 1000em, 2.597em, -0.512em); top: -2.425em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-47" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span><span style="position: absolute; top: -2.059em; left: 0.536em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-48" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; clip: rect(3.005em, 1000em, 3.379em, -0.485em); top: -5.146em; left: 1.125em;"><span style="display: inline-block; position: relative; width: 2.71em; height: 0px;"><span style="position: absolute; font-family: STIXGeneral; top: -3.987em; left: 0em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; font-family: STIXGeneral; top: -3.987em; left: 2.21em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 0.422em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 0.869em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 1.316em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 1.763em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; clip: rect(4.472em, 1000em, 8.446em, -0.485em); top: -6.612em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.184em; height: 0px;"><span style="position: absolute; font-family: STIXNonUnicode; top: -3.32em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; font-family: STIXSizeOneSym; top: -0.681em; left: 0em;">⎷<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXNonUnicode; position: absolute; top: -2.784em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXNonUnicode; position: absolute; top: -2.183em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.634em;"></span></span><span style="position: absolute; clip: rect(1.827em, 1000em, 2.375em, -0.478em); top: -2.375em; left: 0.341em;"><span style="font-size: 50%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-49" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-50" class="mo">≤</span><span style="padding-left: 0.313em;" id="MathJax-Span-51" class="mfrac"><span style="display: inline-block; position: relative; width: 0.713em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(1.533em, 1000em, 2.532em, -0.374em); top: -3.047em; left: 50%; margin-left: -0.296em;"><span style="font-family: STIXGeneral;" id="MathJax-Span-52" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.371em;"></span></span><span style="position: absolute; clip: rect(1.822em, 1000em, 2.595em, -0.471em); top: -1.739em; left: 50%; margin-left: -0.296em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-53" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span><span style="position: absolute; clip: rect(0.849em, 1000em, 1.239em, -0.485em); top: -1.298em; left: 0em;"><span style="border-left: 0.713em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.25px; vertical-align: 0em;"></span><span style="display: inline-block; width: 0px; height: 1.078em;"></span></span></span></span><span style="padding-left: 0.188em;" id="MathJax-Span-54" class="munderover"><span style="display: inline-block; position: relative; width: 1.455em; height: 0px;"><span style="position: absolute; clip: rect(2.096em, 1000em, 3.869em, -0.395em); top: -3.233em; left: 0.027em;"><span style="font-family: STIXSizeOneSym; vertical-align: -0.524em;" id="MathJax-Span-55" class="mo">∑</span><span style="display: inline-block; width: 0px; height: 3.233em;"></span></span><span style="position: absolute; clip: rect(1.564em, 1000em, 2.478em, -0.475em); top: -1.059em; left: 0em;"><span id="MathJax-Span-56" class="texatom"><span id="MathJax-Span-57" class="mrow"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-58" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-59" class="mo">=</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-60" class="mn">1</span></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span><span style="position: absolute; clip: rect(1.636em, 1000em, 2.377em, -0.475em); top: -3.409em; left: 0.512em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-61" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="padding-left: 0.188em;" id="MathJax-Span-62" class="msubsup"><span style="display: inline-block; position: relative; width: 0.988em; height: 0px;"><span style="position: absolute; clip: rect(1.822em, 1000em, 2.597em, -0.512em); top: -2.425em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-63" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span><span style="position: absolute; top: -2.059em; left: 0.536em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-64" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-65" class="mo">≤</span><span style="padding-left: 0.313em;" id="MathJax-Span-66" class="msqrt"><span style="display: inline-block; position: relative; width: 5.427em; height: 0px;"><span style="position: absolute; clip: rect(2.214em, 1000em, 5.406em, -0.485em); top: -3.987em; left: 1.125em;"><span id="MathJax-Span-67" class="mrow"><span id="MathJax-Span-68" class="mfrac"><span style="display: inline-block; position: relative; width: 0.713em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;"><span style="position: absolute; clip: rect(1.533em, 1000em, 2.532em, -0.374em); top: -3.047em; left: 50%; margin-left: -0.296em;"><span style="font-family: STIXGeneral;" id="MathJax-Span-69" class="mn">1</span><span style="display: inline-block; width: 0px; height: 2.371em;"></span></span><span style="position: absolute; clip: rect(1.822em, 1000em, 2.595em, -0.471em); top: -1.739em; left: 50%; margin-left: -0.296em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-70" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span><span style="position: absolute; clip: rect(0.849em, 1000em, 1.239em, -0.485em); top: -1.298em; left: 0em;"><span style="border-left: 0.713em solid; display: inline-block; overflow: hidden; width: 0px; height: 1.25px; vertical-align: 0em;"></span><span style="display: inline-block; width: 0px; height: 1.078em;"></span></span></span></span><span style="padding-left: 0.188em;" id="MathJax-Span-71" class="munderover"><span style="display: inline-block; position: relative; width: 1.455em; height: 0px;"><span style="position: absolute; clip: rect(2.096em, 1000em, 3.869em, -0.395em); top: -3.233em; left: 0.027em;"><span style="font-family: STIXSizeOneSym; vertical-align: -0.524em;" id="MathJax-Span-72" class="mo">∑</span><span style="display: inline-block; width: 0px; height: 3.233em;"></span></span><span style="position: absolute; clip: rect(1.564em, 1000em, 2.478em, -0.475em); top: -1.059em; left: 0em;"><span id="MathJax-Span-73" class="texatom"><span id="MathJax-Span-74" class="mrow"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-75" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-76" class="mo">=</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-77" class="mn">1</span></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span><span style="position: absolute; clip: rect(1.636em, 1000em, 2.377em, -0.475em); top: -3.409em; left: 0.512em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-78" class="mi">n</span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="padding-left: 0.188em;" id="MathJax-Span-79" class="msubsup"><span style="display: inline-block; position: relative; width: 1.494em; height: 0px;"><span style="position: absolute; clip: rect(3.384em, 1000em, 4.306em, -0.512em); top: -3.987em; left: 0em;"><span id="MathJax-Span-80" class="texatom"><span id="MathJax-Span-81" class="mrow"><span id="MathJax-Span-82" class="msubsup"><span style="display: inline-block; position: relative; width: 0.988em; height: 0px;"><span style="position: absolute; clip: rect(1.822em, 1000em, 2.597em, -0.512em); top: -2.425em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-83" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span><span style="position: absolute; top: -2.059em; left: 0.536em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-84" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; top: -2.622em; left: 0.988em;"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-85" class="mn">2</span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; clip: rect(3.005em, 1000em, 3.379em, -0.485em); top: -5.146em; left: 1.125em;"><span style="display: inline-block; position: relative; width: 4.302em; height: 0px;"><span style="position: absolute; font-family: STIXGeneral; top: -3.987em; left: 0em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; font-family: STIXGeneral; top: -3.987em; left: 3.802em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 0.4em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 0.826em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 1.251em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 1.676em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 2.101em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 2.527em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 2.952em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXGeneral; position: absolute; top: -3.987em; left: 3.377em;">‾<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span></span><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; clip: rect(4.472em, 1000em, 8.446em, -0.485em); top: -6.612em; left: 0em;"><span style="display: inline-block; position: relative; width: 1.184em; height: 0px;"><span style="position: absolute; font-family: STIXNonUnicode; top: -3.32em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="position: absolute; font-family: STIXSizeOneSym; top: -0.681em; left: 0em;">⎷<span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXNonUnicode; position: absolute; top: -2.784em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span><span style="font-family: STIXNonUnicode; position: absolute; top: -2.183em; left: 0em;"><span style="display: inline-block; width: 0px; height: 3.987em;"></span></span></span><span style="display: inline-block; width: 0px; height: 4.634em;"></span></span></span></span><span style="font-family: STIXGeneral; padding-left: 0.313em;" id="MathJax-Span-86" class="mo">≤</span><span style="padding-left: 0.313em;" id="MathJax-Span-87" class="munderover"><span style="display: inline-block; position: relative; width: 2.532em; height: 0px;"><span style="position: absolute; clip: rect(1.749em, 1000em, 2.542em, -0.469em); top: -2.371em; left: 0.269em;"><span style="font-family: STIXGeneral;" id="MathJax-Span-88" class="mo">max</span><span style="display: inline-block; width: 0px; height: 2.371em;"></span></span><span style="position: absolute; clip: rect(1.564em, 1000em, 2.544em, -0.406em); top: -1.524em; left: 0em;"><span id="MathJax-Span-89" class="texatom"><span id="MathJax-Span-90" class="mrow"><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-91" class="mn">1</span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-92" class="mo">≤</span><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-93" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="font-size: 70.7%; font-family: STIXGeneral;" id="MathJax-Span-94" class="mo">≤</span><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-95" class="mi">n</span></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span><span style="padding-left: 0.188em;" id="MathJax-Span-96" class="msubsup"><span style="display: inline-block; position: relative; width: 0.988em; height: 0px;"><span style="position: absolute; clip: rect(1.822em, 1000em, 2.597em, -0.512em); top: -2.425em; left: 0em;"><span style="font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-97" class="mi">x<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.003em;"></span></span><span style="display: inline-block; width: 0px; height: 2.425em;"></span></span><span style="position: absolute; top: -2.059em; left: 0.536em;"><span style="font-size: 70.7%; font-family: STIXGeneral; font-style: italic;" id="MathJax-Span-98" class="mi">k<span style="display: inline-block; overflow: hidden; height: 1px; width: 0.012em;"></span></span><span style="display: inline-block; width: 0px; height: 2.209em;"></span></span></span></span></span></span></span><span style="display: inline-block; width: 0px; height: 2.371em;"></span></span></span><span style="border-left: 0em solid; display: inline-block; overflow: hidden; width: 0px; height: 5.72em; vertical-align: -3.362em;"></span></span>

KaTeX

16213 caractères

<span class="katex"><span class="katex-inner"><span class="strut" style="height:2.4185270000000005em;"></span><span class="strut bottom" style="height:5.262037000000001em;vertical-align:-2.84351em;"></span><span class="base textstyle uncramped"><span class="reset-textstyle displaystyle textstyle uncramped"><span class="mop op-limits"><span class="vlist"><span style="top:0.6521079999999999em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord">1</span><span class="mrel">≤</span><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="mrel">≤</span><span class="mord mathit">n</span></span></span></span><span style="top:2.7755575615628914e-17em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span><span class="mop">min</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mord"><span class="mord mathit">x</span><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mrel">≤</span><span class="minner mfrac reset-textstyle displaystyle textstyle uncramped"><span class="vlist"><span style="top:1.5413970000000001em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle cramped"><span class="mord textstyle cramped"><span class="reset-textstyle displaystyle textstyle uncramped"><span class="mop op-limits"><span class="vlist"><span style="top:1.202113em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="mrel">=</span><span class="mord">1</span></span></span></span><span style="top:-0.000005000000000032756em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span><span class="op-symbol large-op mop">∑</span></span></span><span style="top:-1.250005em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathit">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="minner mfrac reset-textstyle displaystyle textstyle uncramped"><span class="vlist"><span style="top:0.686em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle cramped"><span class="mord textstyle cramped"><span class="mord"><span class="mord mathit">x</span><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.677em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle uncramped"><span class="mord textstyle uncramped"><span class="mord">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span></span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.677em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle uncramped"><span class="mord textstyle uncramped"><span class="mord mathit">n</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mrel">≤</span><span class="sqrt mord"><span class="sqrt-sign" style="top:-0.09388000000000007em;"><span class="style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing size1">√</span></span></span><span class="vlist"><span style="top:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:1em;"></span></span><span class="mopen">[</span></span><span style="top:-0.90388em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:1em;"></span></span><span class="reset-textstyle textstyle uncramped sqrt-line"></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:1em;"></span></span></span></span></span><span class="mord mathit">n</span><span class="mclose">]</span><span class="mord displaystyle textstyle uncramped"><span class="mop op-limits"><span class="vlist"><span style="top:1.202113em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="mrel">=</span><span class="mord">1</span></span></span></span><span style="top:-0.000005000000000032756em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span><span class="op-symbol large-op mop">∏</span></span></span><span style="top:-1.250005em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathit">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mord"><span class="mord mathit">x</span><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span></span><span class="mrel">≤</span><span class="minner mfrac reset-textstyle displaystyle textstyle uncramped"><span class="vlist"><span style="top:0.686em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle cramped"><span class="mord textstyle cramped"><span class="mord mathit">n</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.677em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle uncramped"><span class="mord textstyle uncramped"><span class="mord">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mop op-limits"><span class="vlist"><span style="top:1.202113em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="mrel">=</span><span class="mord">1</span></span></span></span><span style="top:-0.000005000000000032756em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span><span class="op-symbol large-op mop">∑</span></span></span><span style="top:-1.250005em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle uncramped"><span class="mord mathit">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mord"><span class="mord mathit">x</span><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mrel">≤</span><span class="sqrt mord"><span class="sqrt-sign" style="top:0.2914679999999996em;"><span class="style-wrap reset-textstyle textstyle uncramped"><span class="delimsizing mult"><span class="vlist"><span style="top:0.6650050000000002em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="delimsizinginner delim-size4"><span>⎷</span></span></span><span style="top:-0.24999499999999975em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="delimsizinginner delim-size4"><span></span></span></span><span style="top:-0.8549949999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="delimsizinginner delim-size4"><span></span></span></span><span style="top:-1.4599949999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="delimsizinginner delim-size4"><span></span></span></span><span style="top:-2.0649949999999997em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="delimsizinginner delim-size4"><span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span></span></span><span class="vlist"><span style="top:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:1em;"></span></span><span class="mord displaystyle textstyle cramped"><span class="minner mfrac reset-textstyle displaystyle textstyle cramped"><span class="vlist"><span style="top:0.686em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle cramped"><span class="mord textstyle cramped"><span class="mord mathit">n</span></span></span></span><span style="top:-0.22999999999999998em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle uncramped frac-line"></span></span><span style="top:-0.677em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle textstyle cramped"><span class="mord textstyle cramped"><span class="mord">1</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mop op-limits"><span class="vlist"><span style="top:1.202113em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="mrel">=</span><span class="mord">1</span></span></span></span><span style="top:-0.000005000000000032756em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span><span class="op-symbol large-op mop">∑</span></span></span><span style="top:-1.250005em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathit">n</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mord"><span class="mord displaystyle textstyle cramped"><span class="mord"><span class="mord mathit">x</span><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span></span><span class="vlist"><span style="top:-0.289em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord">2</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span></span></span><span style="top:-2.3385270000000005em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:1em;"></span></span><span class="reset-textstyle textstyle uncramped sqrt-line"></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:1em;"></span></span></span></span></span><span class="mrel">≤</span><span class="mop op-limits"><span class="vlist"><span style="top:0.6521079999999999em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord scriptstyle cramped"><span class="mord">1</span><span class="mrel">≤</span><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="mrel">≤</span><span class="mord mathit">n</span></span></span></span><span style="top:2.7755575615628914e-17em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span><span class="mop">max</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span><span class="mord"><span class="mord mathit">x</span><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span><span class="reset-textstyle scriptstyle cramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;"></span></span></span></span></span></span></span></span></span>

Zwikix

1805 caractères

<span class='math'><span class='stack'><span class='sign'>min</span><sub>1≤<var>k</var>≤<var>n</var></sub></span> <var>x</var><sub><var>k</var></sub>
≤ <span class='power'><span class='frac'><span class='num'><var>n</var></span><span class='divbar'>/</span><span class='den'><span class='high'><span class='stack'><span class='sign'>∑</span><sub><var>k</var>=1</sub><sup><var>n</var></sup></span></span> <span class='sfrac'><span class='num'>1</span><span class='divbar'>/</span><span class='den'><var>x</var><sub><var>k</var></sub></span></span></span></span> ≤ <span class='bigg radical'><sup><var>n</var></sup><span class='sign'>√</span><span class='radicand'><span class='high'><span class='stack'><span class='sign'>∏</span><sub><var>k</var>=1</sub><sup><var>n</var></sup></span></span> <var>x</var><sub><var>k</var></sub></span></span>
≤ <span class='frac'><span class='num'>1</span><span class='divbar'>/</span><span class='den'><var>n</var></span></span> <span class='high'><span class='stack'><span class='sign'>∑</span><sub><var>k</var>=1</sub><sup><var>n</var></sup></span></span> <var>x</var><sub><var>k</var></sub></span>
≤ <span class='bigg radical'><span class='sign'>√</span><span class='radicand'><span class='hidden'>(</span><span class='sfrac'><span class='num'>1</span><span class='divbar'>/</span><span class='den'><var>n</var></span></span> <span class='high'><span class='stack'><span class='sign'>∑</span><sub><var>k</var>=1</sub><sup><var>n</var></sup></span></span> <span class='power'><var>x</var><sub><var>k</var></sub><sup>2</sup></span><span class='hidden'>)</span></span></span>
≤ <span class='stack'><span class='sign'>max</span><sub>1≤<var>k</var>≤<var>n</var></sub></span> <var>x</var><sub><var>k</var></sub></span>

Comparaison des systèmes d'affichage des formules mathématiques

Rendu visuel

Code final