Homework Help: Finding limit of infinite term

1. The problem statement, all variables and given/known data

The problem is not homework, just something that has been bothering me. It's in picture form, in the attachment.
I'm an undergraduate in math, and this type of convergence is a bit unknown to me. What I've seen so far are normal sequences and series, and power series.
This however, is different, because there is no 'first' term, no 'beginning', so I don't really know how to approach this.

2. Relevant equations

3. The attempt at a solution

The equation I've found that describes this term is:

f(x)^2 = 1 + (x^2)f(x+1)

In this case, we would be looking for f(2). However, that equation doesn't contain enough information to solve it, because there are two free variables.

Any help would be appreciated.