Generating Function for Sequence of Powers of Constant/Examples/2^n

Example of Generating Function for Sequence of Powers of Constant
Let $\sequence {a_n}$ be the sequence defined as:
 * $\forall n \in \Z_{\ge 0}: a_n = 2^n$

That is:
 * $\sequence {a_n} = 1, 2, 4, 8, \ldots$

Then the generating function for $\sequence {a_n}$ is given as:
 * $\map G z = \dfrac 1 {1 - 2 z}$

Proof
A specific instance of Generating Function for Sequence of Powers of Constant:
 * $\map G z = \dfrac 1 {1 - 2 z}$