Ch 21: Series of Constants

About This Chapter

The lessons in this chapter define harmonic and alternating series and describe testing convergence and divergence. Take the lesson quizzes and chapter exam to see how well you are doing in evaluating series.

Series of Constants - Chapter Summary and Learning Objectives

This chapter dives into complicated series theories. Follow along with our expert instructors as they explore methods for testing limits to determine if they are convergent or divergent. Use the self-assessments to see how well you understand the key topics covered in the videos. The topics in this course include:

  • How to use expanded form in math
  • The definition of a harmonic series and its formula
  • Understanding alternating series
  • Identifying terms of series using rectangle areas
  • How to test for convergence/divergence with the ratio test or comparing series

Video Objective
What is Expanded Form in Math? - Definition & Examples This video discusses how to deconstruct numbers into their component parts according to the value of individual digit places.
Harmonic Series in Math: Definition & Formula Instructors discuss standard harmonic and alternating harmonic series, providing examples of each.
Alternating Series with Error Bound Here you'll learn how to use the alternating series test to determine convergence.
Terms of Series as Areas of Rectangles In this video the instructors describe the relationship of improper integrals to series as areas of rectangles and how to use the integral test for convergence.
How to Apply the Ratio Test for Convergence & Divergence This lesson looks for absolute convergence in a series using the ratio test.
Testing for Convergence & Divergence by Comparing Series Finally, the instructors describe how to use more than one series to test convergence through comparison.

5 Lessons in Chapter 21: Series of Constants
Test your knowledge with a 30-question chapter practice test
What is Expanded Form in Math? - Definition & Examples

1. What is Expanded Form in Math? - Definition & Examples

In this lesson, we'll review place value and find out how it's useful when writing numbers in expanded form. We'll also look at a few examples of numbers written out in expanded form.

Convergence & Divergence of a Series: Definition & Examples

2. Convergence & Divergence of a Series: Definition & Examples

In this lesson, we motivate the concept of an infinite series by showing an example from basic physics. We use the example to introduce the geometric series and to further suggest the issues of convergence and divergence. This section is intended to be a preview of series in general. Convergence and divergence extends to all series outside the geometric type.

Harmonic Series in Math: Definition & Formula

3. Harmonic Series in Math: Definition & Formula

The harmonic series provides one of the most important counter-intuitive examples in the study of mathematics. In the harmonic series, the numbers or terms get closer and closer to zero, while the series itself diverges.

How to Apply the Ratio Test for Convergence & Divergence

4. How to Apply the Ratio Test for Convergence & Divergence

Watch this video lesson, and you'll learn how you can use the ratio test to help you determine whether a particular series converges or diverges. You will also learn what to watch out for when using the ratio test.

Testing for Convergence & Divergence by Comparing Series

5. Testing for Convergence & Divergence by Comparing Series

Comparing a series that you are given to a series that you know the answer to can help you to answer questions quickly and easily. Learn how to do so for convergence and divergence testing.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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