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**How do I multiply power series?**

## Homework Statement

Find the power series:

[tex] e^x arctan(x) [/tex]

## Homework Equations

[tex] e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} [/tex]

[tex] arctan(x) = 0 + x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7}[/tex]

## The Attempt at a Solution

So do I multiply 1 by 0, x by x and so forth? Or do I go 1 by 0, 1 by x? Or is there another way?

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