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这几道高数极限题,求解(需详细过程) 30
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1²/n³+2²/n³+3²/n³+......+n²/n³
=(1²+2²+3²+......+n²)/n³
=[n(n+1)(2n+1)/6]/n³
=(1+1/n)(2+1/n)/6
lim1²/n³+2²/n³+3²/n³+......+n²/n³
=lim(1+1/n)(2+1/n)/6
=(1+0)(2+0)/6
=2/6
=1/3
=(1²+2²+3²+......+n²)/n³
=[n(n+1)(2n+1)/6]/n³
=(1+1/n)(2+1/n)/6
lim1²/n³+2²/n³+3²/n³+......+n²/n³
=lim(1+1/n)(2+1/n)/6
=(1+0)(2+0)/6
=2/6
=1/3
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