1/2009—1/2010+1/2008-1/2009+1/2007-1/2008+1/2006-1/2007+1/2005-1/2006+...+1/4-1/5+1/3-1/4+1/2-1/3+1
=1/2+1-1/2010=3014/2010=1507/1005