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+2008)(b+2008)

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+2008)(b+2008)
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+2008)(b+2008)

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+2008)(b+2008)
|ab-2|与|b-1|互为相反数,因绝对值不可能为负数,所以 |ab-2|与|b-1|均为0,b=1,a=2.
1/ab+1/（a+1）（b+1）+1/（a+2）（b+2）+…+1/(a+2008)(b+2008)
=1/1*2 + 1/2*3 + 1/3*4 + ...+ 1/2009*2010
=(1 - 1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ...+ (1/2009 - 1/2010)
=1-1/2010
=2009/2010