The alternating series test is a method used to determine if an infinite series converges or diverges. It states that if the terms of an alternating series decrease in magnitude and approach zero, then the series converges.
Imagine you are playing a game where you have to throw darts at a target. Each time you throw a dart, it either lands on the bullseye or misses completely. If your throws get closer and closer to the bullseye and never miss completely, then your overall score will converge to a specific value.
Convergence: A sequence or series is said to converge if its terms approach a finite limit as the index increases.
Divergence: A sequence or series is said to diverge if its terms do not approach a finite limit as the index increases.
Absolute Convergence: A series is absolutely convergent if the sum of the absolute values of its terms converges.
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