I'd really like your help with this following problem: Let ${a_n}$ be a Fibonacci series $a_1=a_0=1$ and $a_{n+2}=a_n+a_{n+1}$ for every $n \geq 0$.
Let $f(x)=\sum_{0}^{\infty}a_nx^n$, I need to find the radius of convergence and to prove that in the range of this radius $f(x)= \frac{1}{1-x-x^2}$.
we know that the convergence radius $R=\lim_{n\to \infty} |\frac {a_n}{a_{n+1}}| $, How can I apply it in this case? Any direction to prove that $f(x)$ is as requested?
Thanks alot!