Question

用夹逼准则求lim(1/n^2+1/(n^2+1)+...+1/(2n)^2)，n趋向于无穷大

求大神~谢谢啦

Answer 1

1/(4n)=n/(2n)^2<1/n^2+1/(n^2+1)+...+1/(2n)^2<n/n^2=1/n

因为lim(1/(4n))=lim(1/n)=0
所以
原极限=lim(1/n^2+1/(n^2+1)+...+1/(2n)^2)=0