1/3*5+1/5*7+1/7*9+...+1/2003*2005
=1/2[（1/3-1/5)+(1/5-1/7)+(1/7-1/9)...+(1/2003-1/2005)]
=1/2[1/3-1/2005]
=1/2*2002/6015
=1001/6015