Lim（(1²＋2²＋……＋n²)/n³）n→∞＝

Lim（(1²＋2²＋……＋n²)/n³）n→∞＝
Lim（(1²＋2²＋……＋n²)/n³）n→∞＝

Lim（(1²＋2²＋……＋n²)/n³）n→∞＝
1²＋2²＋……＋n²=n(n+1)(2n+1)/6
所以原式=limn(n+1)(2n+1)/6n^3
=lim(1+1/n)(2+1/n)/6
=1*2/6
=1/3