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
![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](/uploads/image/z/16036614-54-4.jpg?t=%E6%94%BE%E7%BC%A9%E6%B3%95%E8%AF%81%E4%B8%8D%E7%AD%89%E5%BC%8F%E6%B1%82%E8%AF%81%EF%BC%9A3%2F2-1%2F%28n%2B1%29%EF%BC%9C1%2B1%2F%282%5E2%29%2B1%2F%283%5E2%29%2B%E2%80%A6%E2%80%A6%2B1%2Fn%5E2%EF%BC%9C2-1%2Fn)
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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