lim(n→∞){n*[1/(n+1)^2+1/(n+2)^2+…1/(n+n)^2]}
=lim(n→∞)(1/n)*{n^2*[1/(n+1)^2+1/(n+2)^2+…1/(n+n)^2]}
=lim(n→∞)(1/n)*{[n/(n+1)]^2+[n/(n+2)]^2+…[n/(n+n)]^2}
=lim(n→∞)(1/n)*{1/(1+1/n)]^2+[1/(1+2/n)]^2+…[1/2]^2}
=lim(n→∞)(1/n)*{(1^2+1^2+…[1/2]^2}(1^2有（n-1）个)
=lim(n→∞)(1/n)*{（n-1）+1/4}
=lim(n→∞)[（n-1）/n]+1/4*lim(n→∞)(1/n)
=lim(n→∞)(1-1/n)
=1
答：请查看附件里的操作步骤.详情>>
答：详情>>
