|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011| 计算
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![|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011| 计算](/uploads/image/z/240094-46-4.jpg?t=%7C1%2F2-1%7C%2B%7C1%2F3-1%2F2%7C%2B%7C1%2F4-1%2F3%7C%2B%7C1%2F5-1%2F4%7C%2B%E2%80%A6%2B%7C1%2F2012-1%2F2011%7C+%E8%AE%A1%E7%AE%97)
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011| 计算
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011| 计算
|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011| 计算
去绝对值,可得 1-1/2+1/2-1/3+1/3-1/4……+1/2011-1/2012=2011/2012.