由a-2=0 b-1=0
解得a=2b=1
所以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)+……+(1/2013-1/2014)
=1-1/2014
=2013/2014