What is this series called? $\frac{x^1}{1!}-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!} \dots \pm \frac{x^n}{n!}$ 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 $\sin{x}$.

Are you sure you didn't get the summands flipped?
The following series is called the Taylor series expansion of $\sin{x}$:
\begin{align*}
\sin{x} &= x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots \\
&= \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!}x^{2n+1} \\[8pt]
\end{align*}
It's derived here.
