# Coefficient in a Power Series

1. Sep 29, 2009

### greenteacup

1. The problem statement, all variables and given/known data

The function
$$f(x)=\frac{1}{1+x^{9}}$$
can be expanded in a power series
$$\sum^{\infty}_{0} a_{n}x^{n}$$
with center c = 0.
Find the coefficient
$$a_{27}$$
of
$$x^{27}$$
in this power series.

2. The attempt at a solution

I can get to:

$$\sum^{\infty}_{0} (-1)^{n}(-x^{9})^{n}$$

which I think is right, but I'm not sure how to find $$a_{27}$$. We didn't talk about it in class.

Last edited: Sep 29, 2009
2. Sep 29, 2009

### Dick

You don't want (-1)^n and (-x^9)^n to both have a '-' in them do you? What are the first few terms in the series when you write them out? a_27 is the coefficient of x^27, which is the n=3 term in your series. What is it?

3. Sep 29, 2009

### greenteacup

Ohhh, okay, I think I understand now. So the coefficient would just be $$(-1)^{3}=-1$$?

4. Sep 29, 2009

Right.