We have given a power series $\sum\limits_{n=0}^\infty a_nx^n$ and $a_0\ne0$. Suppose the power series has radius of convergence $R>0$. Then we may assume that $a_0=1.$
Explanation: It's $\sum\limits_{n=0}^\infty a_nx^n=a_0\sum\limits_{n=0}^\infty \frac {a_n}{a_0}x^n$
But why do $\sum\limits_{n=0}^\infty \frac {a_n}{a_0}x^n$ and $\sum\limits_{n=0}^\infty a_nx^n$ have the same radius of convergence $R$ ?