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