Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

VRAI ou FAUX ?

by mathman·
80
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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Pour k∈Nk\in \mathbb{N} , on se donne une suite de termes uku_{k}

Si lorsque n∈Nn\in\mathbb{N} tend vers +∞+\infty,

Sn=∑k=0nuk\displaystyle S_{n}=\sum_{k=0}^{n}u_{k} converge vers une limite L

alors

Sn′=∑k=0nukn!2(n−k)!(n+k)!\displaystyle S'_{n}=\sum_{k=0}^{n}u_{k}\frac{n!^{2}}{(n-k)!(n+k)!} converge aussi vers L .

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