1/2*4+1/4*6+1/6*8+.+1/2002*2004+1/2004*2006
=（1/2-1/4+1/4-1/6+1/6-1/8+……+1/2002-1/2004+1/2004-1/2006）÷2
=（1/2-1/2006）÷2
=501/2006