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The given series is: $1 - \frac{1}{2} + \frac{1}{4} - \frac{1}{8} + \frac{1}{16} - \dots$
This is a geometric series because each term is obtained by multiplying the previous term by a constant ratio.

The first term of the series is $a = 1$.
The common ratio $r$ can be found by dividing any term by its preceding term:
$r = \frac{-\frac{1}{2}}{1} = -\frac{1}{2}$
$r = \frac{\frac{1}{4}}{-\frac{1}{2}} = -\frac{1}{2}$

A geometric series converges if the absolute value of its common ratio $|r|$ is less than 1.
Here, $r = -\frac{1}{2}$.
So, $|r| = \left|-\frac{1}{2}\right| = \frac{1}{2}$.
Since $\frac{1}{2} < 1$, the series converges.

The given series converges.