Lesson 10: The Ratio Test

Preview

Lesson Preview

  • In this lesson we’ll discuss the Ratio Test (Module 1). This is perhaps the most useful series convergence test. It gives us information about the convergence/divergence of a series depending on whether the limit of the ratio of successive terms in the series is a number less than or greater than 1. (We’ll see that L’Hopital’s Rule (which we covered in the previous lesson) comes in very handy when using the Ratio Test.) Finally, we’ll also review the tests covered thus far and when to use which test (Module 2).

Learn

The lesson notes below contain a learning plan with three stages -- Learn, Reflect, and Practice -- and guidance for what to do within each stage. Some tips for you as you work through this resource, and those that it points to:

  • I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.

Lesson Notes

Lesson 10.pdf

Video 1 (Example 10.1)

Video 2 (Example 10.2)

Reflect

If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:

  • Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.

  • Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.

If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:

  • Please summarize the main mathematical takeaways from the lesson notes.

  • What was the most interesting part of what you learned, and why?

  • What, if anything, do you still find confusing?

Practice

Work through the practice problems suggested below to see how much of this lesson you've understood.

Lesson 10 PP.pdf