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