已知lab-2l+la-2l=0,求1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+```+1/(a+2006)(b+2006)的值
人气：312 ℃ 时间：2020-05-01 05:34:16
解答
a-2=0；a=2；ab-2=0；2b=2；b=1；1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+```+1/(a+2006)(b+2006)=1/(1×2)+1/(2×3)+1/(3×4)+...+1/(2007×2008)=1-1/2+1/2-1/3+1/3-1/4+.+1/2007-1/2008=1-1/2008=2007/2008
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