已知|ab-2|与|b-1|互为相反数,求代数式:1/ab+1/(a+1)*(b+1)+1/(a+2)*(b+2)+···
问题描述：
已知|ab-2|与|b-1|互为相反数,求代数式:1/ab+1/(a+1)*(b+1)+1/(a+2)*(b+2)+···
···+1/(a+2013)*(b+2013)的值
答
|ab-2|=|b-1|=0
a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2013)(b+2013)
=1-1/2015=2014/2015请告诉我理由|ab-2|=|b-1|=0a=2，b=11/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2013)(b+2013)= 1/1x2+1/2x3 +1/3x4 +…+1/2014x2015= 1- 1/2 + 1/2-1/3 +1/3-1/4 + ....+ 1/2014-2015=1-1/2015=2014/2015