91. 求极限 $\lim\limits_{n\rightarrow\infty}\frac{1}{n}\sum_{k=1}^{n}\sin\sqrt{k/n}$.
Posted by haifeng on 2014-09-21 15:57:56 last update 2014-12-28 22:06:22 | Answers (2) | 收藏
求极限
\[\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{k=1}^{n}\sin\sqrt{\frac{k}{n}}.\]
\[
\lim_{n\rightarrow\infty}\biggl(\frac{\sin\frac{\pi}{n}}{n+1}+\frac{\sin\frac{2\pi}{n}}{n+\frac{1}{2}}+\cdots+\frac{\sin\pi}{n+\frac{1}{n}}\biggr).
\]