1/1x2=1-1/2,1/2x3=1/2-1/3,1/3x4=1/3-1/4.那么1/2x4+1/4x6+1/6x8.

=1/2*(1/2-1/4+1/4-1/6+1/6-1/8+……+1/2004-1/2006)+1/2006-1/2007
=1/2*(1/2-1/2006)+1/2006-1/2007
=1/4+1/4012-1/2007
=502754/2013021
=0.24975