Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

Développement en série entière de 1/cos(x)

by mathman·
60
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Montrez que pour ∣x∣<π|x|<\pi :

14cos⁡(x/2)=∑k=0+∞x2kL(2k+1)π2k+1\dfrac{1}{4\cos(x/2)}=\sum\limits_{k=0}^{+\infty}x^{2k}\dfrac{L(2k+1)}{\pi^{2k+1}} où L(n)=∑k=0+∞(−1)k(2k+1)nL(n)=\sum\limits_{k=0}^{+\infty}\dfrac{(-1)^{k}}{(2k+1)^{n}}

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