Alternating Series Test

Equation
$$\sum_{n = 1}^{oo} (-1)^{n-1} a_{n}$$

Use
Will converge if both of the following conditions are true.$$a_{n} \geq a_{n + 1} \geq 0$$$$\lim_{n \rightarrow oo} a_{n} = 0$$If one of the previous tests are failed then it is divergent.If the series converges both with and without the alternator the series is labeled as “Absolutely ConvergentIf the series only converges with alternating series test then it is “Conditionally Convergent.</ol>

Explanation
In a alternating series every term will have a sign different than the term before it. This will cause many terms to cancel each other out. Since the terms are continuously getting smaller, and cancelling out, the series will converge.

Video Explanation


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