@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-RSVD2K5W-N
  skos:narrower psr:-WC4L568R-G ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Divergent_series>, <https://fr.wikipedia.org/wiki/S%C3%A9rie_divergente> ;
  skos:definition """En mathématiques, une série infinie est dite <b>divergente</b> si la suite de ses sommes partielles n'est pas convergente.
<br/>En ce qui concerne les séries de nombres réels, ou de nombres complexes, une condition nécessaire de convergence est que le terme général de la série tende vers 0. Par contraposition, cela fournit de nombreux exemples de séries divergentes, par exemple celle dont tous les termes valent 1. Un exemple de série divergente dont le terme général tend vers 0 est la série harmonique&nbsp;:
<br/>
<br/><center>
<br/><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle 1+{1 \\\\over 2}+{1 \\\\over 3}+{1 \\\\over 4}+{1 \\\\over 5}+\\\\cdots \\\\ =\\\\ \\\\sum _{n=1}^{\\\\infty }\\\\ {\\rac {1}{n}}.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mn>1</mn>
<br/>        <mo>+</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mn>2</mn>
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<br/>        </mrow>
<br/>        <mo>+</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
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<br/>        <mo>+</mo>
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<br/>        <mo>+</mo>
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<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mn>5</mn>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>+</mo>
<br/>        <mo>⋯<!-- ⋯ --></mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <mo>=</mo>
<br/>        <mtext>&nbsp;</mtext>
<br/>        <munderover>
<br/>          <mo>∑<!-- ∑ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>=</mo>
<br/>            <mn>1</mn>
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<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
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<br/>        <mtext>&nbsp;</mtext>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
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<br/>      </mstyle>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle 1+{1 \\\\over 2}+{1 \\\\over 3}+{1 \\\\over 4}+{1 \\\\over 5}+\\\\cdots \\\\ =\\\\ \\\\sum _{n=1}^{\\\\infty }\\\\ {\\rac {1}{n}}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a3f8a450006b9062f06f6049a224ed69a4cb93a3" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:38.316ex; height:6.843ex;" alt="{\\\\displaystyle 1+{1 \\\\over 2}+{1 \\\\over 3}+{1 \\\\over 4}+{1 \\\\over 5}+\\\\cdots \\\\ =\\\\ \\\\sum _{n=1}^{\\\\infty }\\\\ {\\rac {1}{n}}.}"> </center>
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/S%C3%A9rie_divergente">https://fr.wikipedia.org/wiki/S%C3%A9rie_divergente</a>)"""@fr, """In mathematics, a <b>divergent series</b> is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.
<br/>If a series converges, the individual terms of the series must approach zero. Thus any series in which the individual terms do not approach zero diverges. However, convergence is a stronger condition: not all series whose terms approach zero converge. A counterexample is the harmonic series
<br/>
<br/><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle 1+{\\rac {1}{2}}+{\\rac {1}{3}}+{\\rac {1}{4}}+{\\rac {1}{5}}+\\\\cdots =\\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n}}.}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mn>1</mn>
<br/>        <mo>+</mo>
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<br/>          <mfrac>
<br/>            <mn>1</mn>
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<br/>        <mo>+</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
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<br/>        <mo>+</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mn>4</mn>
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<br/>        <mo>+</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
<br/>            <mn>5</mn>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>+</mo>
<br/>        <mo>⋯<!-- ⋯ --></mo>
<br/>        <mo>=</mo>
<br/>        <munderover>
<br/>          <mo>∑<!-- ∑ --></mo>
<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi>n</mi>
<br/>            <mo>=</mo>
<br/>            <mn>1</mn>
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<br/>          <mrow class="MJX-TeXAtom-ORD">
<br/>            <mi mathvariant="normal">∞<!-- ∞ --></mi>
<br/>          </mrow>
<br/>        </munderover>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mn>1</mn>
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<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle 1+{\\rac {1}{2}}+{\\rac {1}{3}}+{\\rac {1}{4}}+{\\rac {1}{5}}+\\\\cdots =\\\\sum _{n=1}^{\\\\infty }{\\rac {1}{n}}.}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b9f5be9aa56324d5f16b4d96c9aea0da0bba24b" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -3.005ex; width:35.8ex; height:6.843ex;" alt="1 + \\rac{1}{2} + \\rac{1}{3} + \\rac{1}{4} + \\rac{1}{5} + \\\\cdots =\\\\sum_{n=1}^\\\\infty\\rac{1}{n}."> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Divergent_series">https://en.wikipedia.org/wiki/Divergent_series</a>)"""@en ;
  skos:broader psr:-B3GGSQMX-3 ;
  skos:inScheme psr: ;
  skos:prefLabel "série divergente"@fr, "divergent series"@en ;
  dc:modified "2023-08-03"^^xsd:date ;
  a skos:Concept ;
  dc:created "2023-08-03"^^xsd:date .

psr:-WC4L568R-G
  skos:prefLabel "harmonic series"@en, "série harmonique"@fr ;
  a skos:Concept ;
  skos:broader psr:-RSVD2K5W-N .

psr:-B3GGSQMX-3
  skos:prefLabel "série"@fr, "series"@en ;
  a skos:Concept ;
  skos:narrower psr:-RSVD2K5W-N .