求极限lim_(ntoinfty)((n)/(1^2)+sqrt(1)+n^(2)+(n)/(2^2)+sqrt(2)+n^(2)+...+(n)/(n^2)+sqrt(n)+n^(2)).

lim_(ntoinfty)((1)/(sqrt(n^2)+1)+(1)/(sqrt(n^2)+2)+...+(1)/(sqrt(n^2)+n))=_.$\li

求极限lim_(ntoinfty)(sqrt[n]((1^2+n^2)(2^2+n^2)...(n^2+n^2)))/(1+2+...+n).求极限$\lim_

12.证明lim_(ntoinfty)((1)/(sqrt(n^2)+1)+(1)/(sqrt(n^2)+2)+...+(1)/(sqrt(n^2)+n))=1

求极限lim_(ntoinfty)(sqrt[n]((n+1)(n+2)...(n+n)))/(n).求极限$\lim_{n\to\infty}\frac{\s

注 类似地，求极限lim_(ntoinfty)sqrt[n](((1^2+n^2)(2^2+n^2)...(n^2+n^2))/(1+2+...+n))注 类似

【例】求极限lim_(ntoinfty)((1)/(n+1)+(1)/(n+sqrt(2))+...+(1)/(n+sqrt(n)))。【例】求极限$\lim_

求极限 lim _(n arrow infty) (sqrt(n^2)+a^(2))/(n)=________.求极限 $\lim _{n \rightarro

3.lim_(ntoinfty)sqrt[n](2+(-1)^n+2^n)=_.3.$\lim_{n\to\infty}\sqrt[n]{2+(-1)^{n}+

2.lim_(ntoinfty)(sqrt(1+2+3+...+n))/(n+2)=( )A. $\frac{1}{2}$B. $\frac{\sqrt{2

例2.11 求下列极限:-|||-(4)lim _(narrow infty )(sqrt ({n)^2+n}-sqrt ({n)^2-n})