递推估计

icesheep

来自贴吧。数列 $\left\{ {{a_{nk}}} \right\}_{k = 1}^n$ 首项为 ${a_{n0}} = \frac{1}{2}$ 且满足递推 \[{a_{n,k + 1}} = {a_{nk}} + \frac{1}{n}a_{nk}^2\]
证明：$1 - \frac{1}{n} < {a_{nn}} < 1$

kuing

forum.php?mod=viewthread&tid=66