已知(ab-2)^2+b-1的绝对值=0

问题描述:

已知(ab-2)^2+b-1的绝对值=0
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2011)(b+2011)

(ab-2)^2+|b-1|=0都是非负数∴b=1ab=2a=21/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2011)(b+2011)=1/1x2+1/2x3+1/3x4+..+1/2012x2013=1-1/2+1/2-1/3+1/3-1/4+...+1/2012-1/2013=1-1/2013=2012/2013...