Answer
$\sum_{n=0}^{\infty} \frac{(-1)^n}{2^n}$ converges absolutely.
Work Step by Step
We have
$$\sum_{n=0}^{\infty} |\frac{(-1)^n}{2^n}|=\sum_{n=0}^{\infty} (\frac{1}{2})^n$$
which is a geometric series with $|r|=|1/2|\lt 1$, which converges.
Then $\sum_{n=0}^{\infty} \frac{(-1)^n}{2^n}$ converges absolutely.
