The Maclaurin Series of an inverse polynomial function

[kudoushinichi88]

Let

$$f(x)=\frac{1}{x^2+x+1}$$

Let $f(x)=\sum_{n=0}^{\infty}c_nx^n$ be the Maclaurin series representation for $f(x)$. Find the value of $c_{36}-c_{37}+c_{38}$.

After working out the fraction, I arrived at the following,

$$f(x)=\sum_{n=0}^{\infty}x^{3n}-\sum_{n=0}^{\infty}x^{3n+1}$$

But I dun get how to compare this to the the form given in the question to get the answer...

 

[tiny-tim]

hi kudoushinichi88!

After working out the fraction

you mean (1-x)/(1 - x³)?

I arrived at the following,

$$f(x)=\sum_{n=0}^{\infty}x^{3n}-\sum_{n=0}^{\infty}x^{3n+1}$$

But I dun get how to compare this to the the form given in the question to get the answer...

but isn't that just c_3n = 1, c_3n+1 = -1, c_3n+2 = 0 ?