5.1 Introduction to Infinite Sequences

In this lesson, you will learn about infinite sequences.

Lesson Objectives

  • Become proficient in the terminology and notation of sequences (including but not limited to: terms, subscripts, recurrence relations, explicit formulas, increasing, decreasing, nonincreasing, nondecreasing, monotonic, bounded).
  • Establish convergence or divergence of a sequence by analyzing limits.
  • Identify a geometric sequence and establish convergence or divergence.
  • Use the Bounded Monotonic Sequence Theorem to establish convergence of bounded monotonic sequences.


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 Sequence? Basic Sequence Info
  2. YouTube video: Sequences – Examples Showing Convergence or Divergence
  3. YouTube video: Finding the Limit of a Sequence
  4. YouTube video: Intro to Monotonic and Bounded Sequences
  5. YouTube video: Bounded, Monotone Sequences
  6. YouTube video: A Quick Intro to Geometric Sequences


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. Sequences
  2. More on Sequences
  3. Sequences
  4. Infinite Sequences, by Dr. Philippe B. Laval
  5. Infinite Sequences
  6. Converging & Diverging Sequences
  7. Convergence and Divergence of Sequences

Additional Resources

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

  1. YouTube video: Monotonic and Bounded Sequences
  2. Sequences: Convergence – definition of convergence, divergence, boundedness
  3. Lecture 2: Convergence of a Sequence, Monotone Sequences