1-1/2+1/3-1/4+.+1/(2n-1)-1/2n=1/(n+1)+1/(n+2)+1/(3+n).+1/2n
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![1-1/2+1/3-1/4+.+1/(2n-1)-1/2n=1/(n+1)+1/(n+2)+1/(3+n).+1/2n](/uploads/image/z/11521077-69-7.jpg?t=1-1%2F2%2B1%2F3-1%2F4%2B.%2B1%2F%EF%BC%882n-1%29-1%2F2n%3D1%2F%28n%2B1%29%2B1%2F%28n%2B2%EF%BC%89%2B1%2F%EF%BC%883%2Bn%29.%2B1%2F2n)
1-1/2+1/3-1/4+.+1/(2n-1)-1/2n=1/(n+1)+1/(n+2)+1/(3+n).+1/2n
1-1/2+1/3-1/4+.+1/(2n-1)-1/2n=1/(n+1)+1/(n+2)+1/(3+n).+1/2n
1-1/2+1/3-1/4+.+1/(2n-1)-1/2n=1/(n+1)+1/(n+2)+1/(3+n).+1/2n
数学归纳法
n=1时成立 1-1/2=1/(1+1)
n=k时若成立
则n=k+1时
左边=1/(k+1)+...+1/2k+1/(2k+1)-1/2(k+1)
=1/(k+2)+...+1/(2k+1)+1/2(k+1)
因此n=k+1时也成立
因此原式成立