已知|ab-2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2013)(b+2013)的值

已知|ab-2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2013)(b+2013)的值
已知|ab-2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2013)(b+2013)的值

已知|ab-2|与|b-1|互为相反数,试求代数式1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2013)(b+2013)的值
∵|ab-2|与|b-1|互为相反数
∴|ab-2|+|b-1|=0
ab-2=0 b-1=0
∴b=1
a=2
∴1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+…+1/(a+2013)(b+2013)
=1/1*2+1/2*3+1/3*4+1/4*5+.+1/2013*2014
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+.+1/2013-1/2014
=1-1/2014
=2013/2014