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

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