7.2 Properties of Power Series

In this lesson, you will learn elementary properties of power series.

Lesson Objectives

  • Identify the radius and interval of convergence of a power series.
  • Use properties of convergent geometric series to construct power series.
  • Establish and use properties of convergent power series.
  • Establish and use the Term-by-Term Differentiation and Integration property of convergent power series.

Lesson Content

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

  1. YouTube videos: Power Series – Radius and Interval of Convergence
    Part 1:

    Part 2:

  2. YouTube video: Power series – Finding the Interval of Convergence
  3. YouTube video: Power Series – Radius of Convergence
  4. YouTube video: Differentiating and Integrating Power 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. Power Series
  2. Power Series and Functions
  3. Power Series and Interval of Convergence
  4. Power Series (definition, examples, theorem)
  5. Power Series – More examples
  6. Radius and Interval of Convergence of Power Series
  7. Properties of Power 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.

Power Series and Radius of Convergence (with solutions)

Additional Resources

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

  1. Review: Power Series
  2. Lesson 21.1: Power Series
  3. The Interval and Radius of Convergence of a Power Series