根据绝对值为非负数得ab-2=0 b-1=0b=1 a=2于是1/ab+1/（a+1)(b+1)+1/(a+2)(b+2)+.1/(a+2010)(b+2010)=1/1x2+1/2x3+1/3x4+.+1/2011x2012=1-1/2+1/2-1/3+1/3-1/4+.+1/2011-1/2012=1-1/2012=2011/2012