丨1/3-1/2丨+丨1/4-1/3丨+丨1/5-1/4丨+...+丨1/2010-1/2009丨
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/2009-1/2010
=1/2-1/2010
=1005/2010-1/2010
=502/1005