|1/2-1|+|1/3-1/2|+|1/4-1/3|+……+|1/2012-1/2011|+|1/2013-1/2012|
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/2011-1/2012)+(1/2012-1/2013)
=1+(1/2-1/2)+(1/3-1/3)+(1/4-1/4)+……+(1/2012-1/2012)-1/2013
=1-1/2013
=2012/2013
内部抵消
1-1/2013=2012/2013