a-1=0
b-2=0
∴a=1
b=2
ab分之1+ （a+1)(b+1)分之1+（a+2)(b+2)分之1+····+（a+2012)(b+2012)分之1
=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