n趋于无穷 lim n[1/(n^2+1)+1/(n^2+2)+……+1/2n^2] 求极限
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根据数列极限的夹逼性
因为n[1/(n^2+1)+1/(n^2+2)+...+1/2n^2]
<n[1/(n^2+1)+1/(n^2+1)+...+1/(n^2+1)]
=n^3/(n^2+1)
且n[1/(n^2+1)+1/(n^2+2)+...+1/2n^2]
>n[1/2n^2+1/2n^2+...+1/2n^2]
=n^3/2n^2
=n/2
因为n^3/(n^2+1)和n/2都趋向于+∞
所以原式也趋向于+∞
因为n[1/(n^2+1)+1/(n^2+2)+...+1/2n^2]
<n[1/(n^2+1)+1/(n^2+1)+...+1/(n^2+1)]
=n^3/(n^2+1)
且n[1/(n^2+1)+1/(n^2+2)+...+1/2n^2]
>n[1/2n^2+1/2n^2+...+1/2n^2]
=n^3/2n^2
=n/2
因为n^3/(n^2+1)和n/2都趋向于+∞
所以原式也趋向于+∞
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