Question

计算:|1/2012-1/2011|+|1/2011-1/2010|+|1/2010-1/2009||+…+|1/3-1

Answer 1

解

因为绝对值非负

所以去掉绝对值符号后必须确保非负

所以

原式=|1/2012-1/2011|+|1/2011-1/2010|+|1/2010-1/2009||+…+|1/3-1/2|+|1/2-1|

=（1/2011-1/2012）+(1/2010-1/2011)+(1/2009-1/2010)+.+(1/2-1/3)+(1-1/2)

=1-1/2012

=2011/2012