Multiplying power series - Maclaurin series

Hi, I've run into some trouble trying to answer this power series question that asks:

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the given function.

This is my work so far (all sums are n=0 to infinity):

=

=

and

=

=

=

To find the first 3 non-zero terms, I think I'm supposed to do something like the following:

n=3

n=2

n=1

n=0

What I got from doing that was:

( becomes -1 for all n)

n=3

=

=

n=2

=

=

n=1

=

n=0

How do I get my 3 terms from the above? I have a lot of fractions where I'm dividing by 0.

Edit: I just realized that I changed into a power series, would the Maclaurin series for that function be the same?