Answer
Converges Absolutely
Work Step by Step
First, Use the alternating Series test
$\Sigma^{\infty}_{n=1} \frac{(-1)^n}{2^n} $
i.) $ a_{n+1} = \frac{1}{2^{n+1}} \leq \frac{1}{2^n} = a_n$
ii.) $\lim\limits_{n \to \infty} \frac{1}{2^n} =0$
Converges by alternating Series test
Now test for conditional or absolute convergence
$|\frac{(-1)^n}{2^n}| \leq (\frac{1}{2})^n$,
Using the Direct Comparison Test, since $ \Sigma^{\infty}_{n=0} (\frac{1}{2})^n$ Converges, then the other must also converge
Converges Absolutely
