Finding the power series for: $f(x) = \frac{1}{2 + x^2}$ at $c=0$
Solution after using substitution of a geometric series with $u= \frac{-1}{2}{x^2}$:
$$f(x) = \frac{1}{2}\sum_{n=0}^\infty \left(\frac{-x^2}{2}\right)^n$$
$$ = \sum_{n=0}^\infty \frac {(-1)^n x^{2n}}{2^{n+1}}$$
But this solution isn't of the form $f(x) = a_n (x - c)^n $ as x is $x^2$ even if $c = 0$.
What am I missing?