对这道题怎么解-----|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2010-
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![对这道题怎么解-----|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2010-](/uploads/image/z/5912638-70-8.jpg?t=%E5%AF%B9%E8%BF%99%E9%81%93%E9%A2%98%E6%80%8E%E4%B9%88%E8%A7%A3-----%7C1%2F2-1%7C%2B%7C1%2F3-1%2F2%7C%2B%7C1%2F4-1%2F3%7C%2B%7C1%2F5-1%2F4%7C%2B.%2B%7C1%2F2010-)
对这道题怎么解-----|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2010-
对这道题怎么解-----|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2010-
对这道题怎么解-----|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2010-
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2010-1/2009|
=1-1/2+1/2-1/3+.+1/2009-1/2010
=1-1/2010
=2009/2010