Unit 8 - Sections 9.5 and 9.6 - Convergence Tests Galore

Module Overview

In the sections covered in this unit, we do two things. First, we examine more convergence tests on positive (or non-negative) series. The tests range from ugly to beautiful, but are all useful. In the second section, we open up to the idea of allowing negative terms in our series and find that this leads to some very odd complications.

Learning Outcomes

Section 9.5: In this section, we learn four closely-related convergence tests. The Comparison Test sets the stage for the proofs of the other three and is occasionally necessary (but often rather ugly). The Limit Comparison and Ratio Tests are rather neat-and-tidy - they tend to be the tests that you will go to first, they are easy to use, and still have a tremendous amount of computational power.
Section 9.6: In this section, we find that when we allow series to take on both positive and negative values, things get very interesting. We explore some of the more far-reaching consequences in a video about math magic, but the amount needed for class is rather lower.

Type: Video Links
Title	Author	Description
The Major Tests - The Comparison Test: A First Look \| The Major Tests - The Comparison Test: A First Look	Shai Cohen
The Major Tests - The Comparison Test \| The Major Tests - The Comparison Test	Shai Cohen
The Major Tests - Limit Comparison Test \| The Major Tests - Limit Comparison Test	Shai Cohen
The Major Tests - The Ratio Test \| The Major Tests - The Ratio Test	Shai Cohen
The Major Tests - The Root Test \| The Major Tests - The Root Test	Shai Cohen
The Major Tests Example - Comparison Test: Ugly \| The Major Tests Example - Comparison Test: Ugly	Shai Cohen
The Major Tests Example - Comparison Test: Necessary Evil \| The Major Tests Example - Comparison Test: Necessary Evil	Shai Cohen
The Major Tests Example - Limit Comparison: Rarely Ugly \| The Major Tests Example - Limit Comparison: Rarely Ugly	Shai Cohen
The Major Tests Example - Limit Comparison: Ugly \| The Major Tests Example - Limit Comparison: Ugly	Shai Cohen
The Major Tests Example - Ratio Test: Easy \| The Major Tests Example - Ratio Test: Easy	Shai Cohen
Series with Negative Terms - The Leibniz Test \| Series with Negative Terms - The Leibniz Test	Shai Cohen
Series with Negative Terms - Magic! \| Series with Negative Terms - Magic!	Shai Cohen
Series with Negative Terms - Absolute Convergence \| Series with Negative Terms - Absolute Convergence	Shai Cohen
Series with Negative Terms Example - Absolute Convergence \| Series with Negative Terms Example - Absolute Convergence	Shai Cohen
Series with Negative Terms Example - Approximating Sums: Optional \| Series with Negative Terms Example - Approximating Sums: Optional	Shai Cohen