求|1/3-1/2|+|1/4-1/3|+1/5-1/4|+.+|1/2012-1/2011|的值

题目

求|1/3-1/2|+|1/4-1/3|+1/5-1/4|+.+|1/2012-1/2011|的值

答案

原式=[(1/2)-(1/3)]+[(1/3)-(1/4)]+[(1/4)-(1/5)]+……+[(1/2011)-(1/2012)]
=(1/2)-(1/2012)
=(1006-1)/2012
=1005/2012.