f(1+1)=f(1)*f(1)
f(2)=f(1)=1
f(3)=f(2+1)=f(2)*f(1)=1
f(3)=1
.
f(1)=f(2)=f(3)=f(4)=...=f(2009)
f(2)/f(1)+f(3)/f(2)+…f(2009)/f(2008)
=1+1+...+1
=2008