Assessing Whether the Series $\sum_\limits{n = 0}^\infty (-1)^n x^{2n} = 1 – x^2 + x^4 – x^6 + \dots$ Converges (conditional/absolute) or Diverges

Question

It's been a while since I've used the various tests for convergence (conditional/absolute) and divergence, and I can't remember which test needs to be used and how to assess whether the series $\sum_\limits{n = 0}^\infty (-1)^n x^{2n} = 1 – x^2 + x^4 – x^6 + \dots$ converges (conditionally/absolutely) or diverges?

I would appreciate it if people could please explain the test that I need to use, why this test needs to be used (within this context), and how it is used (within this context).

Addition:

From Thomas's Calculus, 14th Edition:

Answer 1

$$\sum_\limits{n = 0}^\infty (-1)^n x^{2n} = 1 - x^2 + x^4 - x^6 + \dots$$

is a geometric series which converges to $$\frac {1}{1+x^2}$$ for $|x|<1$ and diverges otherwise.