Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

A perturbed recurrent sequence

by Baked_Baguette·translated by visitor·
40
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
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  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
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Let (un)\left(u_n\right) be a real sequence such that un+1−sin⁡(un)→0u_{n+1}-\sin \left(u_n\right) \rightarrow 0 as n→+∞n \rightarrow+\infty. Show that un→0u_n \rightarrow 0 as n→+∞n \rightarrow+\infty.

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