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