|a-1|+(ab-2)2=0
∴a-1=0
ab-2=0
∴a=1
b=2
∴1/ab +1/(a +1)(b+ 1)+ 1/(a+ 2)(b+ 2)+ …… +1/(a+ 2012)(b +2012)
=1/1×2+1/2×3+1/3×4+……+1/2013×2014
=1-1/2+1/2-1/3+1/3-1/4+……+1/2013-1/2014
=1-1/2014
=2013/2014