求1/(x+1)(x+2)+1/(x+3)(x+4)+...+1/(x+1999)(x+2000)的值
求1/(x+1)(x+2)+1/(x+3)(x+4)+...+1/(x+1999)(x+2000)的值
数学人气：643 ℃时间：2019-12-09 00:36:03
优质解答
=1/(x+1)-1/(x+2)+1/(x+2)-1/(x+3)+1/(x+3)-1/(x+4)+1/(x+4)-1/(x+5)...+1/(x+1998)-1/(x+1999)+1/(x+1999)-1/(x+2000) =1/(x+1)-1/(x+2000) =1999/(x+1)(x+2000) =1999/(x^2+2001x+2000)
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