已知绝对值ab+2与绝对值a+1的和为0,求1/（a-1)(b+1)+1/(a-2)(b+2)+...+1/(a-2009)(b+2009)的值
问题描述：
已知绝对值ab+2与绝对值a+1的和为0,求1/（a-1)(b+1)+1/(a-2)(b+2)+...+1/(a-2009)(b+2009)的值
答
∵|ab+2|+|a+a|=0,|ab+2|≥0,|a+1|≥0∴|ab+2|=0,|a+1|=0∴ab=-2,a=-1∴b=21/（a-1)(b+1)+1/(a-2)(b+2)+...+1/(a-2009)(b+2009)=-1/(2*3)-1/(3*4)-...-1/(2010*2011)=1/3-1/2+1/4-1/3+...+1/2011-1/2010=-1/2+1/2011...