用放缩法证明:1/2-1/(n+1)

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用放缩法证明:1/2-1/(n+1)
用放缩法证明:1/2-1/(n+1)

用放缩法证明:1/2-1/(n+1)
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/(1*2)+1/(2*3)+````+1/[(n-1)*n]
=1-1/2+1/2+1/3+……+1/(n-1)-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)

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