放缩法证不等式求证:3/2-1/(n+1)<1+1/(2^2)+1/(3^2)+……+1/n^2<2-1/n
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放缩法证不等式
求证:3/2-1/(n+1)<1+1/(2^2)+1/(3^2)+……+1/n^2<2-1/n
求证:3/2-1/(n+1)<1+1/(2^2)+1/(3^2)+……+1/n^2<2-1/n
1+1/2²+1/3²+...+1/n²
>1+1/(2×3)+1/(3×4)+...+1/[n(n+1)]
=1+(1/2-1/3)+(1/3-1/4)+...+(1/n-1/(n+1))
=1+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)
=(3/2)-1/(n+1)
1+1/2²+1/3²+...+1/n²
>1+1/(2×3)+1/(3×4)+...+1/[n(n+1)]
=1+(1/2-1/3)+(1/3-1/4)+...+(1/n-1/(n+1))
=1+1/2-1/3+1/3-1/4+...+1/n-1/(n+1)
=(3/2)-1/(n+1)
1+1/2²+1/3²+...+1/n²
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