|2/1-1|+|3/1-2/1|+4/1-3/1|+|5/1-4/1|+…+|2012/1-20
=1-(1/2)+(1/2)-(1/3)+(1/3)-(1/4)+(1/4)-(1/5)+……+(1/2011)-(1/2012)
=1-(1/2012)
=2011/2012