$R_n(x) = \frac{f^{(n)}(0)}{n!}x^n$

$R_n(x) = \frac{f^{(n+1)}(c)}{(n+1)!}x^{n+1}$ for some $c$ between $0$ and $x$

$R_n(x) = \frac{x^{n+1}}{(n+1)!}$

$R_n(x) = e^x - P_n(x)$ where $P_n$ is the $n$-th partial sum