|a-1|+|ab-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+2011)(b+2011)
=1-1/2+1/2-1/3+.+1/2012-1/2013
=1-1/2013=2012/2013
|a-1|+|ab-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+2011)(b+2011)
=1-1/2+1/2-1/3+.+1/2012-1/2013
=1-1/2013=2012/2013