用数学归纳法证明1/(1x3)+1/(3x5)+1/(5x7)…1/(2n-1)(2n+1)=n/(2n+1)我证明完n=k+1后与结论不符,不知哪错了当n=k时成立即1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)=k/(2k+1)则n=k+1时1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)+1/(2k+1
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![用数学归纳法证明1/(1x3)+1/(3x5)+1/(5x7)…1/(2n-1)(2n+1)=n/(2n+1)我证明完n=k+1后与结论不符,不知哪错了当n=k时成立即1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)=k/(2k+1)则n=k+1时1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)+1/(2k+1](/uploads/image/z/11482734-30-4.jpg?t=%E7%94%A8%E6%95%B0%E5%AD%A6%E5%BD%92%E7%BA%B3%E6%B3%95%E8%AF%81%E6%98%8E1%2F%281x3%29%2B1%2F%283x5%29%2B1%2F%285x7%29%E2%80%A61%2F%282n-1%29%282n%2B1%29%3Dn%2F%282n%2B1%29%E6%88%91%E8%AF%81%E6%98%8E%E5%AE%8Cn%3Dk%2B1%E5%90%8E%E4%B8%8E%E7%BB%93%E8%AE%BA%E4%B8%8D%E7%AC%A6%2C%E4%B8%8D%E7%9F%A5%E5%93%AA%E9%94%99%E4%BA%86%E5%BD%93n%3Dk%E6%97%B6%E6%88%90%E7%AB%8B%E5%8D%B31%2F%281x3%29%2B1%2F%283x5%29%2B1%2F%285x7%29%E2%80%A61%2F%282k-1%29%282k%2B1%29%3Dk%2F%282k%2B1%29%E5%88%99n%3Dk%2B1%E6%97%B61%2F%281x3%29%2B1%2F%283x5%29%2B1%2F%285x7%29%E2%80%A61%2F%282k-1%29%282k%2B1%29%2B1%2F%282k%2B1)
用数学归纳法证明1/(1x3)+1/(3x5)+1/(5x7)…1/(2n-1)(2n+1)=n/(2n+1)我证明完n=k+1后与结论不符,不知哪错了当n=k时成立即1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)=k/(2k+1)则n=k+1时1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)+1/(2k+1
用数学归纳法证明1/(1x3)+1/(3x5)+1/(5x7)…1/(2n-1)(2n+1)=n/(2n+1)
我证明完n=k+1后与结论不符,不知哪错了
当n=k时成立
即1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)=k/(2k+1)
则n=k+1时
1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)+1/(2k+1)(2k+3)
=k/(2k+1)+1/(2k+1)(2k+3)
=2k^2+3k+1/(2k+1)(2k+3)
=(k+1/2)(k+1)/(2k+1)(2k+3)
=(k+1)/2(2k+3)
而原式应为(k+1)/(2k+3)
用数学归纳法证明1/(1x3)+1/(3x5)+1/(5x7)…1/(2n-1)(2n+1)=n/(2n+1)我证明完n=k+1后与结论不符,不知哪错了当n=k时成立即1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)=k/(2k+1)则n=k+1时1/(1x3)+1/(3x5)+1/(5x7)…1/(2k-1)(2k+1)+1/(2k+1
=k/(2k+1)+1/(2k+1)(2k+3)
=(2k+1)(k+1/(2k+3))
=(2k+1)((2k方+3k+1)/(2k+3))
=1/(2k+1)*((2k+1)(k+1)/(2k+3))
=(k+1)/(2k+3)成立
你算的
=(2k^2+3k+1)/(2k+1)(2k+3)
=(2k+1)(k+1)/(2k+1)(2k+3)
=(k+1)/(2k+3)
哪来的1/2