用夹逼求极限
由于k∑[k=1->n]k/(n^2+1)=n(n+1)/[2(n^2+1)]->1/2 (n->∞),∑[k=1->n]√[k(k+1)/(n^2+1)n](k+1)/(n^2+1)=n(n+3)/[2(n^2+1)]->1/2 (n->∞).因此由夹逼定理原式极限为1/2.