Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

Une limite à la fois étrange et imposante

by Sequoia·
45
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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Montrer que la quantité suivante est définie et la calculer:
lim⁡x→+∞(∑n=1+∞(xn)n)1x.\underset{x\rightarrow+\infty}{\lim}\left(\displaystyle\sum_{n=1}^{+\infty}\left(\frac{x}{n}\right)^n\right)^{\frac{1}{x}}.

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