1/(2×4)+1/4×6+1/(6×8)……+1/(2006×2008)
=(1/2-1/4)/2+(1/4-1/6)/2+91/6-1/8)/2+...+(1/2006-1/2008)/2
=(1/2-1/2008)/2
=1003/2008*1/2
=1003/4016