求极限 $\lim\limits_{n\rightarrow\infty}\biggl[\frac{1}{n+1}+\frac{1}{(n^2+1)^{1/2}}+\cdots+\frac{1}{(n^n+1)^{1/n}}\biggr]$
求极限
\[
\lim_{n\rightarrow\infty}\biggl[\frac{1}{n+1}+\frac{1}{(n^2+1)^{1/2}}+\cdots+\frac{1}{(n^n+1)^{1/n}}\biggr]
\]
[Hint] 使用夹逼准则.