已知|ab - 2|与|b -1|互为相反数,求1/ab+1/(a+1) (b+1)+1/(a+2) (b+2)+.1/(a+2003) (b+2003)

题目

已知|ab - 2|与|b -1|互为相反数,求1/ab+1/(a+1) (b+1)+1/(a+2) (b+2)+.1/(a+2003) (b+2003)

答案

绝对值是大于等于0的
ab-2=0,b-1=0
a=2,b=1
1/ab+1/(a+1) (b+1)+1/(a+2) (b+2)+.1/(a+2003) (b+2003)
=(1-1/2)+(1/2-1/3)+……+(1/2004-1/2005)
=1-1/2005
=2004/2005