Let $\omega$ be a root of unity and $p \in \mathbb{N}^*$. Let $\sum_{n=0}^{+\infty} R(n) x^n$ denote the power series expansion of $\frac{1}{(1 - \omega x)^p}$. Show that $R$ is a quasi-polynomial function then determine its degree and its leading coefficient.
Let $\omega$ be a root of unity and $p \in \mathbb{N}^*$. Let $\sum_{n=0}^{+\infty} R(n) x^n$ denote the power series expansion of $\frac{1}{(1 - \omega x)^p}$. Show that $R$ is a quasi-polynomial function then determine its degree and its leading coefficient.