求极限 lim n[1/(n^2+1)+1/(n^2+2^2)+……+1/(n^n+n^n)] (n趋向于无穷大,n^n表示n
问题描述:
求极限 lim n[1/(n^2+1)+1/(n^2+2^2)+……+1/(n^n+n^n)] (n趋向于无穷大,n^n表示n
答
=lim n^2·[1/(n^2+1)+1/(n^2+2^2)+……+1/(n^n+n^n)] /n=lim [n^2/(n^2+1)+n^2/(n^2+2^2)+……+n^2/(n^n+n^n)]·(1/n) =lim [1/(1+(1/n)^2) +1/(1+(2/n)^2) +……+ 1/(1+(n/n)^2))]·(1/n)=∫《x从0到1》1/(1+x...