|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+…+|1/2012-1/2011|
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/2011-1/2012
=1-1/2012
=2011/2012