(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm just trying to understand a few things about the Maclaurin series for e^x...

So, in one case, if you have a series from 1 to infinity of [(-1)^n * 3^n ]/n!, how is it that it is equal to e^-3 - 1? I understand the e^-3 part, as -3 is simply our x value from the series. Is the negative one simply because the series starts at 1, or does it have something to do with the alternating portion of the series? I'm a bit confused there...

And then say we have xe^x. If I wanted to find the Maclaurin series for this one, well, I know that the value that e is raised to will take the place of x in the series. As for the x hanging out in the front, do I simply add that to the series? So the series would be from 0 to infinity, x^n+1 / n!

I guess I'm just looking for some general rules when dealing with the Maclaurin series for e^x...

Any help in the right direction would be great.

Thanks!

2. Relevant equations

e^x = series (0 to infinity) x^n/n!

3. The attempt at a solution

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# Homework Help: Maclaurin Series for e^x

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