因为(a-1)^2+|a+b-2|=0
所以a-1=0,a=1
a+b-2=0,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+...+1/(a+2008)(b+2008)
=1+1/4+1/9+1/16.+1/2008^2