Question

当n趋向于无穷大时，求（1＋2²＋3²＋…＋n²)/n³ 极限

Answer 1

1＋2²＋3²＋…＋n²=n(n+1)(2n+1)/6

所以原式=1/3

Answer 2

lim[n→+∞]（1＋2²＋3²＋…＋n²)/n³
=lim[n→+∞]n(n+1)(2n+1)/(6n^3)
=lim[n→+∞]1(1+1/n)(2+1/n)/6
=1/3