# The Maclaurin Series of an inverse polynomial function

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...

## Answers and Replies

tiny-tim
Homework Helper
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 c3n = 1, c3n+1 = -1, c3n+2 = 0 ?