I remember learning about this series in Precalculus the other day but I neglected to get the name of it. It looks something like this:
$ \begin{align*} \frac{x^1}{1!}-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!} \dots \pm \frac{x^n}{n!} \end{align*} $
All I remember is that it helps in the modeling of $\sin{x}$.