|1/2-1|+|1/3-1/2|+|1/4-1/3|+......+|1/2012-1/2011|

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提示：困歼肢1/(n+1)<1/n，因此|1/(n+1) -1/n|=1/n -1/(n+1)

|1/2-1|+|1/3-1/2|+|1/4-1/3|+......+|1/2012-1/2011|
=1-1/改睁2+1/2-1/3+1/汪世3-1/4+...+1/2011-1/2012
=1-1/2012
=2011/2012

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