5.2 Introduction to Infinite Series

In this lesson, you will learn about infinite series.

Lesson Objectives

• Given an infinite sequence, construct the sequence of partial sums and recognize that an infinite series is a sequence of the partial sums.
• Recognize that convergence of an infinite series is equivalent to the convergence of a sequence of partial sums.
• Identify a geometric series and establish its convergence or divergence.
• Identify a telescoping series and establish its convergence.
• Recognize that convergent series have the linearity property identical to definite integrals.

Lesson Content

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

1. YouTube video: What is a Series?
2. Geometric Series
3. YouTube videos: Geometric Series for the Test for Divergence
Part 1:

Part 2:

4. YouTube video: Telescoping Series, Finding the Sum
5. YouTube video: Telescoping Series Example
6. YouTube video: Telescoping Series, Showing Divergence Using Partial Sums

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. Series
2. Infinite Series
3. Chapter 2: Infinite Series  – properties of convergence and divergent series
4. Infinite Series , by J. Robert Buchanan – definition of infinite series, convergence and divergence, geometric series, issues of convergence and divergence

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- Series (Introduction) – determining the convergence of the series (with solutions)
2. Sequences, Geometric and Telescoping Series  Do #5 & # 6.

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

1. Brightstorm videos: Geometric Series
Concept:

Problem 1:

Problem 2:

Problem 3:

2. Infinite Series , by Dr. Philippe B. Laval
3. Infinite Series , by J. Robert Buchanan – definition of infinite series, convergence and divergence, geometric series, issues of convergence and divergence