Generating Function for Constant Sequence/Examples

Examples of Generating Function for Constant Sequence

$a_0 = 1, a_n = 2$

Let $\sequence {a_n}$ be the sequence defined as:

$\forall n \in \Z_{\ge 0}: a_n = \begin{cases} 1 & : n = 0 \\ 2 & : n > 0 \end{cases}$

Then the generating function for $\sequence {a_n}$ is given as:

$\map G z = \dfrac {1 + z} {1 - z}$