Let's use this basic generating function to find generating functions for more sequences. What if we replace \(x\) by \(-x\text{.}\) We get

\begin{equation*} \frac{1}{1+x} = 1 - x + x^2 - x^3 + \cdots \mbox{ which generates } 1, -1, 1, -1, \ldots\text{.} \end{equation*}