The Maclaurin series for $e^x$ is a Taylor series expansion of $e^x$ around $x = 0$. The Maclaurin series is given by:

$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$

This can be written out explicitly as:

$e^x = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots$

Do you want more details or have any questions?

Here are some related questions:

1. What is the general form of a Maclaurin series for any function?
2. How can the Maclaurin series be used to approximate $e^x$ for small values of $x$?
3. What is the radius of convergence of the Maclaurin series for $e^x$?
4. How does the Maclaurin series for $e^x$ relate to its derivatives?
5. Can you find the Maclaurin series for other exponential functions like $e^{-x}$?

Tip: When using the Maclaurin series for practical calculations, truncating the series after a few terms often provides a good approximation, especially for small values of $x$.