|1∕1001-1∕1000|+|1∕1002-1∕1001|-|1∕1002-1∕1000|,|为绝对值

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|1∕1001-1∕1000|+|1∕1002-1∕1001|-|1∕1002-1∕1000|,|为绝对值|1∕1001-1∕1000|+|1∕1002-1∕1001|-|1∕1002-1∕1000|

|1∕1001-1∕1000|+|1∕1002-1∕1001|-|1∕1002-1∕1000|,|为绝对值
|1∕1001-1∕1000|+|1∕1002-1∕1001|-|1∕1002-1∕1000|,|为绝对值

|1∕1001-1∕1000|+|1∕1002-1∕1001|-|1∕1002-1∕1000|,|为绝对值
|1∕1001-1∕1000|+|1∕1002-1∕1001|-|1∕1002-1∕1000|
=1/1000-1/1001+1/1001-1/1002-1/1000+1/1002
=0
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去掉绝对之后:1/1000--1/1001+1/1001--1/1002--1/1000+1/1002=0