数学题解答|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2004-1/2003|

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数学题解答|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2004-1/2003|

数学题解答|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2004-1/2003|
数学题解答|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2004-1/2003|

数学题解答|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2004-1/2003|
1001/2004

|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2004-1/2003|
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+…+(1/2003-1/2004)
=1/2-1/2004
=1001/2004

原式=1/2-1/2004=1001/2004

去绝对值符号后就是1/2-1/3+1/3-1/4+1/4-1/5+...........+1/2003-1/2004=1/2-1/2004=1001/2004

原式=1/2-1/3+1/3-1/4+1/4-1/5+。。。。。。+1/2003-1/2004=1/2-1/2004=1001/2004