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

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/23 10:59:45
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)+

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