/ab-2/+/b-1/=0
∴﹛ab-2=0
b-1=0
∴b=1,a=2
∴1/ab+1/(a+1)(b+1)+1/(a+2)(b+2）+...+1/（a+2012)(b+2013)
=1/1x2+1/2x3+1/3x4+……+1/2013x2014
=1-1/2+1/2-1/2-1/3+1/3-1/4+……+1/2013-1/2014
=1-1/2014
=2013/2014