Maclaurin series for $x^6 \cdot e^{-x}$

Question

I am being asked to find a Maclaurin series for $x^6 \cdot e^{-x}$ manually for a homework question and am being asked to do it via a table:

http://www.webassign.net/scalcet/11-10-030.gif

I have no idea how to approach this question. I don't want the answer (I need to DIY) but does anyone have any tips on how to actually go about solving this?

Answer 1

It's not too hard to build it from other series. Your table has the series for $e^x$, so it's a simple matter to change all the $x$'s to $-x$'s and you have the series for $e^{-x}$.