How can I expand $f(x)$ in powers of x? $f(x)=\frac{1-x}{1+x}$. The closest thing I know to this would be $\sum_{k=0}^\infty x^k=\frac{1}{1-x}$ but I don't know how to use it to write $f(x)$
HINT: $$\frac{1-x}{1+x}=1-\frac{2x}{1+x}=1-\frac{2x}{1-(-x)}$$
$f(x)=\frac{1-x}{1+x} = \frac{2}{1+x} - \frac{1+x}{1+x}
= 2g(-x) - 1$ where $g(x) =\frac{1}{1-x}$.

You should be able to take it from there.