即ab-2=0,b-1=0
所以b=1,a=2/b=2
所以原式=1/1*2+1/2*3+1/3/4+……+1/2011*2012
=1-1/2+1/2-1/3+1/3-1/4+……+1/2011-1/2012
=1-1/2012
=2011/2012