2/(2n-1)(2n+1)=1/(2n-1)-1/(2n+1)
2/1*3+2/3*5+2/5*7+.+2/2007*2009
=(1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/2007-1/2009)
=1-1/2009
=2008/2009