6.1 Convergence Tests, Part I

In this lesson, you will learn about convergence tests for infinite series.

Lesson Objectives

• • Correctly apply the Divergence Test.

  • Correctly apply the Integral Test.

  • Identify and establish the divergence of the Harmonic Series.

  • Identify and establish convergence criteria for p series.

Lesson Content

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

• 1. YouTube video: Test for Divergence for Series, Two Examples

• 1. YouTube video: Integral Test- Basic Ideas

• 1. YouTube videos: Integral Test for Series

  2. Example 1

• 2. Example 2:

• 1. YouTube video: Using the Integral Test for Series

• 1. YouTube video: Divergence of the Harmonic Series

• 1. YouTube video: The Integral Test for Series 1b - More Examples/p-Series

  2. Review additional resource #5 if necessary

• 1. YouTube video: P-Series - Defining P-Series

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. Chapter 2: Infinite Series Please read C2 Divergent Tests on pages 3 - 5

  2. Integral Test

  3. The Integral Test

1. Integral Test and p-Series

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.

• 1. Drill- Integral Test Use the integral test to determine the convergence of the series. (10 problems with solutions)

1. 2.4. Improper Integrals and the Integral Test

Additional Resources

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

• 1. The Divergence Test

  2. Integral Test

  3. The Integral Test

  4. The Integral Test Please read part 1.1- The Integral Test and 1.2- Applying the Integral Test.

  5. YouTube video: Improper Integral of 1/x^p The improper integrals that establish the P series convergence or divergence