(1/2-1)+(1/3-1/2)+(1/4-1/3)+.+(1/2014-1/2013)的值

(1/2-1)+(1/3-1/2)+(1/4-1/3)+.+(1/2014-1/2013)的值
(1/2-1)+(1/3-1/2)+(1/4-1/3)+.+(1/2014-1/2013)的值

(1/2-1)+(1/3-1/2)+(1/4-1/3)+.+(1/2014-1/2013)的值
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2014-1/2013|.
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2013-1/2014
=1/2-1/2014
=553/1007
打字不易,

原式=1/2-1+1/3-1/2+1/4-1/3+……+1/2014-1/2013
=-1+1/2014（其他全部抵消）
=-2013/2014

列项法 常规题~~~~~