证明极限(1/(n^2+1/(n^2+1)+1/(n^2+2)+...+1/(n^2+n)的极限=0

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证明极限(1/(n^2+1/(n^2+1)+1/(n^2+2)+...+1/(n^2+n)的极限=0
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证明极限(1/(n^2+1/(n^2+1)+1/(n^2+2)+...+1/(n^2+n)的极限=0
证明极限(1/(n^2+1/(n^2+1)+1/(n^2+2)+...+1/(n^2+n)的极限=0

证明极限(1/(n^2+1/(n^2+1)+1/(n^2+2)+...+1/(n^2+n)的极限=0
1/(n^2+1/(n^2+1)+1/(n^2+2)+...+1/(n^2+n)
<1/n^2+1/n^2+1/n^2+...+1/n^2
=1/n->0
再由本身的非负性,有夹逼定理可证得极限是0