Question

用不定积分求极限

Answer 1

解：∵1/(2n)=n/(n^2+n^2)<1/(n^2+1^2)+1/(n^2+2^2)+.....+1/(n^2+n^2)<n/n^2=1/n
又lim(n->∞)[1/(2n)]=lim(n->∞)[1/n]=0
∴由夹逼定理，得lim(n->∞)[1/(n^2+1^2)+1/(n^2+2^2)+.....+1/(n^2+n^2)]=0。

Answer 2

引用heanmeng的回答：
解：∵1/(2n)=n/(n^2+n^2)<1/(n^2+1^2)+1/(n^2+2^2)+.....+1/(n^2+n^2)<n/n^2=1/n
又lim(n->∞)[1/(2n)]=lim(n->∞)[1/n]=0
∴由夹逼定理，得lim(n->∞)[1/(n^2+1^2)+1/(n^2+2^2)+.....+1/(n^2+n^2)]=0。

答案是π/6