ab-2=0,b-1=0
b=1,a=2
1/ab+1/(a+1)(b+1)+……+1/(a+2006)(b+2006)
=1/1*2+1/2*3+……+1/2007*2008
=(1-1/2)+(1/2-1/3)+……+(1/2007-1/2008)
=1-1/2008
=2007/2008