|a-2|+|b-1|=0
∴a-2=0
b-1=0
∴a=2,b=1
1/ab+1/(a+1)(b+1)+1/(a+2)(b+2)+···+1/(a+2004)(b+2004)
=1/1*2+1/2*3+1/3*4+……+1/2005*2006
=1-1/2+1/2-1/3+1/3-……-1/2005+1/2005-1/2006
=1-1/2006
=2005/2006