已知b-1的相反数等于他本身,ab与-2互为相反数,1/ab+1/(a+1)(b+1)+1/(a+2)(a+2)+.+

问题描述:

已知b-1的相反数等于他本身,ab与-2互为相反数,1/ab+1/(a+1)(b+1)+1/(a+2)(a+2)+.+
1/(a+2013)(a+2013)的值

b-1=-(b-1)
ab-2=0
解得,a=2 ,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+.+1/(a+2013)(b+2013)
=1/(2×1)+1/(3×2)+...+1/(2015×2014)
=1-1/2+1/2-1/3+...+1/2014-1/2015
=1-1/2015
=2014/2015