|1/2-1|+|1/3-1/2|+|1/4-1/3|+|1/5-1/4|...|1/2011-1/2010|
=(1-1/2)+(1/2-1/3)+.+(1/2009-1/2010)+(1/2010-1/2011)
=1-1/2+1/2-1/3+.+1/2009-1/2010+1/2010-1/2011
=1-1/2011
=2010/2011