计算|1/3-1/2|+|1/4-1/3|+|1/5-1/4|.|1/2004-1/2003|.

题目

计算|1/3-1/2|+|1/4-1/3|+|1/5-1/4|.|1/2004-1/2003|.
为什么?为了保险起见我先少加悬赏．如果在今天（10月12日）内给答案,我给五十分以上．

答案

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+1/5-……-1/2004
=1/2-1/2004=1001/2004