We consider a power series $\sum_{n \geqslant 0} \alpha_n z^n$, with radius of convergence $R \neq 0$ and with $\alpha_0 = 1$. We denote by $S$ the sum of this power series on its disk of convergence.
Show that there exists a real number $q > 0$ such that $\forall n \in \mathbb{N}, |\alpha_n| \leqslant q^n$.