Alternating Series

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by stephaniejoy19
Last updated 5 years ago

Discipline:
Math
Subject:
Calculus

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Alternating Series

The video to the right shows us how to test series to see if they are absolutely convergent, conditionally convergent, or just plain old divergent!

Sometimes the series will converge but the absolute value of the series will diverge. If this happens, we say the series is conditionally convergent.

There are three simple conditions to check for when using the Alternating Series Test:1. Do the terms in the series alternate signs?2. Is the absolute value of each term less than/equal to the term that came before it?(Is |an+1| < |an| or is |an+1| = |an|?)3. Is the limit as n approaches infinity of an equal to zero?Answer yes to all the above questions? Then the series converges by the Alternating Series Test!

Alternating Series Test

This video explains the test the same way, he just uses bn instead of an.(And he includes an example)

Now there are three different cases to worry about with alternating series...

1. Absolute Convergence2. Conditional Convergence3. Divergence

This picture shows an example of an alternating series.


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