1/2*4+1/4/6+1/6*8+……+1/2004*2006+1/2006*2008
=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2004-1/2006+1/2006-1/2008)
=1/2*(1/2-1/2008)
=1/2*1003/2008
=1003/4016