原式=（2/1*3+2/3*5+2/5*7+2/7*9+……+2/2001*2003）/2
=（1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+……1/2001-1/2003）/2
=（1-1/2003）/2
=1001/2003