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