 $\displaystyle \lim_{n \rightarrow \infty}
\frac{x^n}{n!} = 0$ for all real $x$.
 $\displaystyle e^x = \sum_{n=0}^{\infty}
\frac{x^n}{n!}$ for all real $x$.
 $\displaystyle e = \sum_{n=0}^{\infty} \frac{1}{n!}$
 The Binomial Series:
If $k$ is any real number and $x< 1$, then
$\displaystyle (1+x)^k = \sum_{n=0}^{\infty}{k \choose
n}\, x^n = 1 + kx + \frac{k(k1)}{2!}x^2 +
\frac{k(k1)(k2)}{3!}x^3 + \ldots$
