1/2x4+1/4x6+1/6x8+...+1/2006x2008
=（1/2-1/4+1/4-1/6+1/6-1/8+……+1/2006-1/2008）÷2
=（1/2-1/2008）÷2
=1003/2008÷2
=1003/4016