|1/2-1/3|+|1/3-1/4|+|1/4-1/5|+…+|1/2014-1/2015|=?
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![|1/2-1/3|+|1/3-1/4|+|1/4-1/5|+…+|1/2014-1/2015|=?](/uploads/image/z/5298928-16-8.jpg?t=%7C1%2F2-1%2F3%7C%2B%7C1%2F3-1%2F4%7C%2B%7C1%2F4-1%2F5%7C%2B%E2%80%A6%2B%7C1%2F2014-1%2F2015%7C%3D%3F)
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|1/2-1/3|+|1/3-1/4|+|1/4-1/5|+…+|1/2014-1/2015|=?
|1/2-1/3|+|1/3-1/4|+|1/4-1/5|+…+|1/2014-1/2015|=?
|1/2-1/3|+|1/3-1/4|+|1/4-1/5|+…+|1/2014-1/2015|=?
|1/2-1/3|+|1/3-1/4|+|1/4-1/5|+…+|1/2014-1/2015|=1/2-1/3+1/3-1/4+1/4-1/5+...+1/2014-1/2015=1/2-1/2015=2013/4030
=1/2-1/3+1/3-1/4+1/4-1/5+....+1/2014-1/2015
=1/2-1/2015
=2015/4030-2/4030
=2013/4030
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1/2-1/2015