Introduction
This test can be used to determine the convergence or divergence of a series whose terms alternate in sign. You can also find the error in an estimated sum of these special series. Additionally we have to look at finding the interval of convergence of power series that are not geometric.
Objective: We address topic 4 (PDF) in the AP course outline. By the end of this section you will be able to determine the convergence or divergence of an alternating series using the Alternating Series Test and determine its absolute or conditional convergence. You will also be able to determine the interval of absolute and conditional convergence of a power series by checking its endpoint series.
Topics in this section include:
- 9-5c.1-2: The Alternating Series Theorem
- Video: Alternating Series
- 9-5c.3-4: Absolute and Conditional Convergence
- Video: Absolute/Conditional Convergence
- 9-5c.5: Reviewing Comparison Tests and When to Use Them
- 9-5c.6: The Alternating Series Remainder Theorem
- 9-5c.7: Interval of Convergence for a Power Series - Basics
- 9-5c.8: Interval of Convergence for a Power Series - Examples
- Video: Power Series - Finding the Interval of Convergence
- Check for Understanding
- 9-5c.9: Too Many Absolutes
- 9-5c.10: Summary of Methods of Determining Convergence and Divergence
- Convergence Tests - Summary and Study Chart
Now that you are familiar with the topics we will cover in this section of Module 9, you are ready to begin. Please click the menu item under Section called The Alternating Series Theorem to begin 9-5c.1-2: The Alternating Series Theorem.
Photo Attribution
Description: A male holding a stack of books with a chalkboard in the background.
Source: iStock.com