In this lesson, you will learn about infinite sequences.
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.
View all of the following instructional videos. These will help you master the objectives for this module.
YouTube video: What is a Sequence? Basic Sequence Info
YouTube video: Sequences - Examples Showing Convergence or Divergence
YouTube video: Finding the Limit of a Sequence
YouTube video: Intro to Monotonic and Bounded Sequences
YouTube video: Bounded, Monotone Sequences
YouTube video: A Quick Intro to Geometric Sequences
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.
Infinite Sequences, by Dr. Philippe B. Laval
Limits of Sequences - using a limit to determine the convergence or divergence of a sequence
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.
Sequences, Geometric and Telescoping Series
Note: Do #1-4.
Below are additional resources that help reinforce the content for this module.
YouTube video: Monotonic and Bounded Sequences
Sequences: Convergence - definition of convergence, divergence, boundedness