TMMATE 2009, Problema 2
Posted: Thu Apr 23, 2009 7:34 pm
Fie sirul \( (a_n)_{n \geq 1} \) pentru care \( a_1=1 \) si \( a_{n+1}=\frac{n}{a_n+1} \) pentru \( n \geq 1 \). Aratati ca:
a) \( a_n \geq \sqrt{n} -1, \forall n \in \mathbb{N}^* \);
b) \( \lim_{n\to\infty} \frac{a_n^2}{n}=1. \)
Laurentiu Panaitopol
a) \( a_n \geq \sqrt{n} -1, \forall n \in \mathbb{N}^* \);
b) \( \lim_{n\to\infty} \frac{a_n^2}{n}=1. \)
Laurentiu Panaitopol