Generating Function for Constant Sequence

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

for some $r \in \R$.

Then the generating function for $\sequence {a_n}$ is given as:
 * $\map G z = \dfrac r {1 - z}$ for $\size z < 1$

Proof
for $\size z < 1$.