|1/2|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+……+|1/2014-1/2013|+|1/2015-1/2014|
=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/20134-1/2014)+(1/2014-1/2015)
=1/2+1/2-1/2015
=2014/2015