化简|1/2-1|+|1/3-1/2|……|1/2000-1/1999

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化简|1/2-1|+|1/3-1/2|……|1/2000-1/1999
化简|1/2-1|+|1/3-1/2|……|1/2000-1/1999

化简|1/2-1|+|1/3-1/2|……|1/2000-1/1999
|1/2-1|+|1/3-1/2|……|1/2000-1/1999|
=1-1/2+1/2-1/3……+1/1999-1/2000
=1-1/2000
=1999/2000