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