lim(n→∞){n/（n^2+1）+n/（n^2+2^2）+....+n/（n^2+n^2）}求此式的极限？说明一下那是n除以n的平方加1,

再加上个n除以n的平方加上2的平方一直加到n除以n的平方加上n的平方。谢谢

原式=lim(n→∞)[(1/n)/(1+(1/n)^2)+(1/n)/(1+(2/n)^2)+...+(1/n)/(1+(n/n)^2)] （每项上下同时除以n^2）
=lim(n→∞)1/n*[1/(1+(1/n)^2)+1/(1+(2/n)^2)+...+1/(1+(n/n)^2)]
=∫(0→1)1/(1+x^2)dx （区间[0,1]的分点为i/n）
=arctanx|(0→1)
=π/4

lim（n→∞）[1/（n^2+n+1）+2/（n^2+n+2）+3/（n^2+n+3）+……+n/（n^2+n+n）] ＝ lim（n→∞）[(1+2+...+n)/（n^2+n+1）] =lim（n→∞）1/2*[n(n+1)/（n^2+n+1）] =1/2

lim(n→∞)n[1/(n^2+1)+1/(n^2+2)+1/(n^2+3)+……+1/(n^2+n)] lim(n→∞)[n/(n^2+1)+n/(n^2+2)+n/(n^2+3)+……+n/(n^2+n)] 对于每一项来说，分子均为一次项，分母为二次项，均趋向0 lim(n→∞)n[1/(n^2+1)+1/(n^2+2)+1/(n^2+3)+……+1/(n^2+n)]=0