|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2013-1/2014|

问题描述:

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2013-1/2014|

原式=(1/2-1/3) +(1/3-/14)+.+(1/2012-1/2013)+(1/2013-1/2014)
=1/2-1/2014
=1006/2014
=503/1007