1＋2²＋3²＋…＋n²=n(n+1)(2n+1)/6所以原式=1/3
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
