初中绝对值|1/2010-1/2009|+|1/2009-1/2008|+...|1/2-1|

问题描述:

初中绝对值|1/2010-1/2009|+|1/2009-1/2008|+...|1/2-1|

|1/2010-1/2009|+|1/2009-1/2008|+...|1/2-1|
=-(1/2010-1/2009)-(1/2009-1/2008)-...-(1/2-1)
=-1/2010+1/2009-1/2009+1/2008-..-1/2+1
=1-1/2010
=2009/2010