Mathematica: Recursive expression

[Niles]

Hi

I am trying to find a smart way to write the following fraction,

$$
F = \frac{a_1}{1+\frac{a_2}{1+\frac{a_3}{1+a_4}}}
$$

Here we can just take [itex]a_n= n[/itex] for simplicity. My fraction is in principle infinite, but I am trying to construct a function which can find [itex]F[/itex] for a given [itex]n[/itex] recursively. I haven't had much success. So far I have

f[n_] := n;
f[n - 1]/(1 + f[n])

which is the last term for a given [itex]n[/itex]. For do I propagate all the way up to [itex]a_1[/itex] then?

 

[Bill Simpson]

Will one of these do what you are looking for?

http://mathematica.stackexchange.com/questions/21998/building-a-continued-fraction

 

[Hepth]

f[1] = Subscript[a, 1];

f[n_] := (f[n - 1]) /.Subscript[a, n - 1] :> Subscript[a, n - 1]/(1 + Subscript[a, n])

Does that work?