=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