x/1*3+x/3*5+x/5*7+.+x/2007*2009=2008
x(1/1*3+1/3*5+1/5*7+.+1/2007*2009)=2008
x[1/2*(1-1/3)+1/2*(1/3-1/5)+1/2*(1/5-1/7)+.+1/2*(1/2007-1/2009)]=2008
x/2(1-1/3+1/3-1/5+1/5-1/7+.+1/2007-1/2009)=2008
x/2(1-1/2009)=2008
x/2*2008/2009=2008
x/2*1/2009=1
x=2*2009
x=4018