The Alternating Series Test

Most of the convergence tests we've seen so far only work on series with positive terms, so how do we test alternating series?
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This video was originally a part of a larger video lecture, so please pardon any out of place references to example problems, etc. that came from these videos' original contexts.
The original lecture this video came from can be found here:
• The Alternating Series...
The full playlist of these Calculus theory videos can be found here:
• Calculus 2 Theory
You can find a playlist of all my Calculus lectures (where these theory videos were originally a part) here:
• Calculus 2 Lectures