Generating Function for Constant Sequence

Theorem
Let $\left \langle {a_n}\right \rangle$ be the sequence defined as:
 * $\forall n \in \N: a_n = r$

for some $r \in \R$.

Then the generating function for $\left \langle {a_n}\right \rangle$ is given as:
 * $G \left({z}\right) = \dfrac r {1 - z}$ for $\left\lvert{z}\right\rvert < 1$

Proof
for $\left|{z}\right| < 1$.