f(2)/f(1)+f(3)/f(2)+.f(2005)/f(2004)
=f(1+1)/f(1)+f(2+1)/f(2)+.f(2004+1)/f(2004)
= f(1)*f(1)/f(1)+f(2)*f(1)/f(2)+.f(2004)*f(1)/f(2004)
=f(1)+f(1)+.+f(1)
=2004*f(1)
f(2)/f(1)+f(3)/f(2)+.f(2005)/f(2004)
=f(1+1)/f(1)+f(2+1)/f(2)+.f(2004+1)/f(2004)
= f(1)*f(1)/f(1)+f(2)*f(1)/f(2)+.f(2004)*f(1)/f(2004)
=f(1)+f(1)+.+f(1)
=2004*f(1)