用放缩法证明: 1/2-1/(n+1)<1/(2^2)+1/(3^3)+````+1/(n^2)<(n-1)/n (n=2,3,````)
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估计你题目打错了。我自己改一下。把3^3改成3^2
1/(2^2)+1/(3^2)+````+1/(n^2)
>
1/(2*3)+1/(3*4)+....+1/[n(n+1)]
=1/2-1/3+1/3-1/4+......+1/n-1/(n+1)
=1/2-1/(n+1)
右半部分
1/(2^2)+1/(3^2)+````+1/(n^2)
<
1/(1*2)+1/(2*3)+....+1/[(n-1)n]
=1-1/2+1/2-1/3.......+1/(n-1)-1/n
=(n-1)/n
1/(2^2)+1/(3^2)+````+1/(n^2)
>
1/(2*3)+1/(3*4)+....+1/[n(n+1)]
=1/2-1/3+1/3-1/4+......+1/n-1/(n+1)
=1/2-1/(n+1)
右半部分
1/(2^2)+1/(3^2)+````+1/(n^2)
<
1/(1*2)+1/(2*3)+....+1/[(n-1)n]
=1-1/2+1/2-1/3.......+1/(n-1)-1/n
=(n-1)/n
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