Originally Posted by

**worc3247** I am having trouble with this question:

Define $\displaystyle F(x)=$\displaystyle\sum\limits_{n=0}^\infty F_nx^n$$ where $\displaystyle F_n$ is the nth Fibonacci number. Determine the radius of convergence of F(x). Using $\displaystyle F_{n+2} = F_{n+1} + F_n$ 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 $\displaystyle x^2-x-1$ i.e. $\displaystyle \frac{2}{1+\sqrt{5}}$?

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)