∵|ab-2|+|1-b|=0
∴ab-2=0,1-b=0
∴ab=2,b=1
∴a=2,b=1
1/ab + 1/(a+1)(b+1) + 1/(a+2)(b+2)+.1/(a+2003)(b+2003)
=1/1×2+1/3×2 +1/4×3+……..+1/2005×2004
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2004-1/2005)
=1-1/2+1/2- 1/3+ 1/3- 1/4+……+1/2004-1/2005
=1-1/2005
=2004/2005