问题

Questions in category: 极限 (Limit).

求极限 $\lim\limits_{n\rightarrow\infty}\frac{1}{n^2}\biggl[\sqrt{n^2-1}+\sqrt{n^2-4}+\cdots+\sqrt{n^2-(n-1)^2}\biggr]$

Posted by haifeng on 2017-04-08 18:57:17 last update 2017-04-08 20:28:42 | Answers (1) | 收藏

求

\[
\lim_{n\rightarrow\infty}\frac{1}{n^2}\biggl[\sqrt{n^2-1}+\sqrt{n^2-4}+\cdots+\sqrt{n^2-(n-1)^2}\biggr]
\]

[Hint] 用积分