|ab-2|+|b-1|=0 1/ab+1/(a+b)(b+1)+1/(a+2)(b+2)+''''''+1/(a+2008)(b+2008)=?
问题描述：
|ab-2|+|b-1|=0 1/ab+1/(a+b)(b+1)+1/(a+2)(b+2)+''''''+1/(a+2008)(b+2008)=?
答
绝对值为非负数,和为0只有分别等于0
ab-2=0,b-1=0
b=1,a=2
原式=1/1×2+1/2×3+1/3×4+1/2009×2010
=1-1/2+1/2-1/3+...+1/2009-1/2010
=1-1/2010
=2009/2010