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)<1/2^2+1/3^2+.+1/n^2<(n-1)/n
用放缩法证明1/2-1/(n+1)
1/2^2+1/3^2+.+1/n^2>1/(2*3)+1/(3*4)+...+1/[n*(n+1)]
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)
1/2^2+1/3^2+.+1/n^2
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)