|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2006-1/2005| 的简便算法
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![|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2006-1/2005| 的简便算法](/uploads/image/z/1263381-69-1.jpg?t=%7C1%2F3-1%2F2%7C%2B%7C1%2F4-1%2F3%7C%2B%7C1%2F5-1%2F4%7C%2B.%2B%7C1%2F2006-1%2F2005%7C+%E7%9A%84%E7%AE%80%E4%BE%BF%E7%AE%97%E6%B3%95)
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2006-1/2005| 的简便算法
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2006-1/2005| 的简便算法
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2006-1/2005| 的简便算法
原式=[-1/2+1/3]+[-1/3+1/4]+[-1/4+1/5]+......+[-1/2005+1/2006]
=-1/2+1/2006
=-2005/2006