|1/2-1|+|1/3-1/2|+|1/4-1/3|+.+|1/2014-1/2013|

|1/2-1|+|1/3-1/2|+|1/4-1/3|+.+|1/2014-1/2013|

把绝对值去掉,然后变为相反数,也就是倒着减
于是原式变为
1-1/2+1/2-1/3+1/3-1/4+……+1/2013-1/2014=1-1/2014=2013/2014

原式=-1/2十1-1/3+1/2-…-1/2014十
1/2013
=1一1/2014
=2013/2014

1/2014-1= - 2013/2014