如题用数学归纳法证明:1/n+1/(1+n)+1/(n+2) +.1/n^2>1(n∈N且n>1)所以当n=k+1时,有:1/n+1/(n+1)+...+1/k^2+1/(k^2+1)+1/(k^2+2)+...+1/(k^2+2k+1)>1+1/(k^2+1)+1/(k^2+2)+1/(k^2+2k+1)这步错了 应当从1/(n+1)开始加应当>1+1/(k^2+1)
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![如题用数学归纳法证明:1/n+1/(1+n)+1/(n+2) +.1/n^2>1(n∈N且n>1)所以当n=k+1时,有:1/n+1/(n+1)+...+1/k^2+1/(k^2+1)+1/(k^2+2)+...+1/(k^2+2k+1)>1+1/(k^2+1)+1/(k^2+2)+1/(k^2+2k+1)这步错了 应当从1/(n+1)开始加应当>1+1/(k^2+1)](/uploads/image/z/1626502-22-2.jpg?t=%E5%A6%82%E9%A2%98%E7%94%A8%E6%95%B0%E5%AD%A6%E5%BD%92%E7%BA%B3%E6%B3%95%E8%AF%81%E6%98%8E%EF%BC%9A1%2Fn%2B1%2F%281%2Bn%29%2B1%2F%28n%2B2%29+%2B.1%2Fn%5E2%3E1%28n%E2%88%88N%E4%B8%94n%3E1%29%E6%89%80%E4%BB%A5%E5%BD%93n%3Dk%2B1%E6%97%B6%2C%E6%9C%89%3A1%2Fn%2B1%2F%28n%2B1%29%2B...%2B1%2Fk%5E2%2B1%2F%28k%5E2%2B1%29%2B1%2F%28k%5E2%2B2%29%2B...%2B1%2F%28k%5E2%2B2k%2B1%29%3E1%2B1%2F%28k%5E2%2B1%29%2B1%2F%28k%5E2%2B2%29%2B1%2F%28k%5E2%2B2k%2B1%29%E8%BF%99%E6%AD%A5%E9%94%99%E4%BA%86+%E5%BA%94%E5%BD%93%E4%BB%8E1%2F%EF%BC%88n%2B1%EF%BC%89%E5%BC%80%E5%A7%8B%E5%8A%A0%E5%BA%94%E5%BD%93%3E1%2B1%2F%28k%5E2%2B1%29)
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