real analysis - Geometric series in closed form.

$$f=\sum_{k=3}^{\infty}(-1)^kx^{(2k-2)}$$

i would like to write this as the geometric power series!

Is there a ritual you have to do to solve this? thanks in advance.

Answer

$$\sum_{k\geq3}\left(-1\right)^{k}x^{2k-2}=\frac{1}{x^{2}}\sum_{k\geq3}\left(-x^{2}\right)^{k}=-x^{4}\sum_{k\geq0}\left(-x^{2}\right)^{k}.$$