Coefficient of $x^r$ in $\frac{1}{(1-ax)^n}$

Question

In my combinatorics class, we were taught that the coefficient of $x^r$ in $\frac{1}{(1-x)^n}$ is $\binom{r+n-1}{r}$. I am struggling to figure out what the coefficient of $x^r$ would be in $\frac{1}{(1-ax)^n}$, where $a \in \mathbb{N}$. I know that the expansion of $\frac{1}{(1-x)^n}$ is $\sum\limits_{k=0}^\infty \binom{k+n-1}{k}x^k$, so my initial thought was that it would be $a^r\binom{r+n-1}{r}$, but I'm not sure. Any help would be appreciated.

Answer 1

Hint: See that coefficient of $x^r$ will be $a^r\binom{r + n - 1}{r}$.