作业帮已知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
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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
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
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
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
lab-2l+la-2l=0
所以ab-2=0,a-2=0
则a=2,b=2/a=1
所以原式=1/1×2+1/2×3+……+1/2007×2008
=1-1/2+1/2-1/3+……+1/2007-1/2008
=1-1/2008
=2007/2008
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