计算过程如下：
用夹逼定理：
S=lim (n→∞) n2[(1/n2+1)2+2/(n2+2)2+n/(n2+n)2]
=lim (n→∞)n2[(1/n2+n)2+2/(n2+n)2+n/(n2+n)2]≤S
≤lim (n→∞)n2[(1/n2+1)2+2/(n2+1)2+n/(n2+1)2]
=lim (n→∞) n2*[n*(n+1)/2]/(n2+n)2]≤S
≤lim (n→∞) n2[n*(n+1)/2]/(n2+1)21/2≤S≤1/2 S=1/2
n→无穷时，为无限项想加n*min≤所有项相加≤n*max =n*(1/n+n)≤所有项相加的和≤n*(1/n+1)
limn→∞(n2+1)+(n2+2)+…+(n2+n)n(n1)(n2)=limn→∞n3+(1+2+3++n)n33n2+2n=limn→∞n3+n2+n2n33n2+2n=1.
用夹逼定理即可
设原极限为I
lim(n/(n^2+1))*n
