当n趋向于无穷大时,求(1+2²+3²+…+n²)/n³ 极限
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当n趋向于无穷大时,求(1+2²+3²+…+n²)/n³ 极限
当n趋向于无穷大时,求(1+2²+3²+…+n²)/n³ 极限
当n趋向于无穷大时,求(1+2²+3²+…+n²)/n³ 极限
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
1+2²+3²+…+n²=n(n+1)(2n+1)/6
所以原式=1/3