|1/3-1/2|+|1/4-1/3|+|1/5-1/4|+...+|1/2010-1/2009|
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/2009-1/2010
=1/2-1/2010
=1004/2010
=502/1005