6.4 Alternating Series

In this lesson, you will learn about alternating series, absolute convergence, and conditional convergence.

Lesson Objectives

• • Identify an alternating series.

  • Correctly apply the Alternating Series Test.

  • Calculate a bound for the remainder of an alternating series.

  • Understand the difference between conditional and absolute convergence.

  • Establish the conditional convergence, absolute convergence, or divergence of an alternating series.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

• 1. YouTube video: Alternating Series

• 1. YouTube video: The Alternating Series Test

• 1. YouTube videos: Alternating Series

  2. Example 1:

• 1. Example 2:

• 1. Example 3:

• 1. Example 4:

• 1. More Examples:

• 1. YouTube video: Absolute Convergence, Conditional Convergence and Divergence

• 1. YouTube videos: Absolute Convergence, Conditional Convergence

  2. Example 1:

• 1. Example 2:

• 1. Example 3:

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

• 1. Alternating Series and Absolute Convergence (convergence theorem for alternating series, estimation of the remainder, absolute versus conditional convergence)

  2. Alternating Series

  3. Alternating Series Test

  4. Alternating Series Test

  5. Absolute and Conditional Convergence

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

Drill - Alternating Series Test

Additional Resources

Below are additional resources that help reinforce the content for this module.

1. Alternating Series

   1. Alternating Series

   2. Alternating Series Test

   3. Absolutely and Conditionally Convergent Series