|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|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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