Name: Infinite Sequences and Series: Alternating Tests
Uploaded: 2022-12-01T18:30:09+00:00
Duration: 2 h 31 min
Description: In this video I go over further into the wonderful world of Infinite Sequences and Series and this time look at Alternating Series; which are series that alternate from positive and negative terms. Wh

3 years ago

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In this video I go over further into the wonderful world of Infinite Sequences and Series and this time look at Alternating Series; which are series that alternate from positive and negative terms. When dealing with alternating positive and negative terms it is important to develop specific theorems and methodologies in order to better analyze whether they converge or diverge. Often times it is best to view the odd and even terms of the series separately since they would have the same signs when grouped together. I go over this and much more throughout the video so make sure to follow along!

The topics and their timestamps in the video are listed below:

- 0:00 - Intro
1. @ 1:28 - Introduction to Alternating Series
2. @ 6:06 - The Alternating Series Test
- @ 14:00 - Proof of the Alternating Series Test
- @ 27:50 - Example 1
- @ 32:03 - Example 2
- @ 36:28 - Example 3
3. @ 53:43 - Estimating Sums
- @ 55:05 - Alternating Series Estimation Theorem
- @ 59:27 - Example 4
- @ 1:11:26 - Important Note
4. Exercises
- @ 1:11:52 - Exercise 1
- @ 1:48:22 - Exercise 2
- @ 2:08:50 - Proof of the Multiplication Rule for Logarithms
- @2:14:05 - Exercise 3