I am having trouble with this question:

Define where is the nth Fibonacci number. Determine the radius of convergence of F(x). Using find F(x) in closed form.

I think I have managed to do the radius of convergence but I don't know if I am correct. Is the answer the solution to i.e. ?

As for the second part I have completely no idea and would appreciate some help starting the question (I should note I have tried writing F(x) out in terms of the formula but have not gotten anywhere with this)