Wright Math

9.6 [10.6]: The Alternating Series Test


Alternating Series:  We’ve seen all kinds of tests now for determining whether or not an infinite series converges or diverges. What none of those tests has taken into account is what effect a flip-flopping sign on the terms has on convergence.

Intuitively, if we add a bit… then subtract a bit less…then add a still smaller amount… and so on, then it should be “easier’ in some sense for the series to add up to be a finite number (hence converge).

What you’ll learn about in the videos is the test for convergence in these Alternating (flip-flopping) Series. Then you’ll learn about the difference between Conditional Convergence (where the flip-flopping of the signs is needed to keep the sum finite) vs. Absolute Convergence (where the flip-flopping isn’t necessary because the terms get small FAST enough).

Videos:

Alternating Series Test

Example

More Examples

 Absolute vs. Conditional Convergence

 

Assigned Problems from Textbook   

Note:  This is a scaled-down set of homework problems as compared to the original assignment sheet.

1st Edition Section 9.6, page 677 

6, 11, 13, 15, 19, 22, 27, 45, 47, 48, 49, 52, 53, 54

3rd Edition Section 10.6, page 688 

6, 11, 13, 15, 19, 22, 27, 45, 48, 51, 54, 57, 58