2/3×1+2/5×3+2/7×5+…+2/2005×2003 =(3-1)/1×3+(5-3)/3×5+(7-5)/5×7…+(2005-2003)/2003×2005 =3/1×3-1/1×3+5/3×5-3/3×5+7/5×7-5/5×7+……+2005/2003×2005-2003/2003×2005 =1-1/3+1/3-1/5+1/5-1/7+……+1/2003-1/2005 =1-1/2005=2004/2005.