|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|等于多少?
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![|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|等于多少?](/uploads/image/z/1668513-57-3.jpg?t=%7C1%2F3-1%2F2%7C%2B%7C1%2F4-1%2F3%7C%2B%7C1%2F5-1%2F4%7C%2B.%2B%7C1%2F2005-1%2F2004%7C%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|等于多少?
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|等于多少?
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|等于多少?
|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+.+|1/2005-1/2004|
=(1/2-1/3)+(1/3-1/4)+...+(1/2004-1/2005)
=1/2-1/2005
=2003/4010
=1/2-1/3+1/3-1/4+……+1/2004-1/2005
=1/2-1/2005
=2003/4010
| 1/3-1/2<0, 所以|1/3-1/2|=-(1/3-1/2)=1/2-1/3
同理,1/4-1/3<0,|1/4-1/3|=1/3-1/4
……
|1/2005-1/2004|=1/2004-1/2005
所以原式=1/2-1/3+1/3-1/4+……+1/2004-1/2005
=1/2-1/2005
=2003/4010
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