Problema 22461 G.M. 9/1991, sir convergent

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Bogdan Cebere
Thales
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Joined: Sun Nov 04, 2007 1:04 pm

Problema 22461 G.M. 9/1991, sir convergent

Post by Bogdan Cebere »

Demonstrati ca sirul \( {d_{n}}=-\ln n+\sum_{k=1}^n\sin{ \frac{1}{k}}\ \) este convergent.

D. M. Batinetu-Giurgiu
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Marius Mainea
Gauss
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Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

Se foloseste sirul lui Euler \( a_n=\sum_{k=1}^n {\frac{1}{k}}-\ln n \) si faptul ca \( \sin x\leq x \) pentru orice \( x\geq 0 \).
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