2.lim_(n to infty)(sqrt(n+1)-sqrt(n))sqrt(n+1)=_____.

[题目]求值 lim _(narrow infty )(sqrt (n+1)-sqrt (n))

[题目]计算 lim _(narrow infty )cos (sqrt (n+1)-sqrt (n))

级数 sum _(n=1)^infty (sqrt (n+2)-2sqrt (n+1)+sqrt (n))= __ .

3.已知 =sqrt (n+1)-sqrt (n) , =sqrt (n+2)-sqrt (n+1) , gt 0 ,试比较a,b的大小.

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

18.-|||-在下列无穷级数中,收敛的级数是 ()-|||-A sum _(n=1)^infty (sqrt (n+1)-sqrt (n));-|||-B s

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

=sqrt (n+2)-sqrt (n+1) , gt 0 ,试比较-|||-a,b的大小.

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