How to Find the Radius & Interval of Convergence for Power Series (Calculus 2 Lesson 31)

In this video we learn about Power Series and how to find their radius and interval of convergence. A power series is a type of series that includes a variable, such as x, raised to a power of n. Because of this included variable, the terms of a power series form a function. This function is only defined for the values of x that make the power series convergent. In order to find these values of x that make the power series convergent (interval of convergence), we will use many of the convergence tests and skills related to series that have been covered up to this point. We discuss how this is will be done, and go over a couple examples explaining and showing the process in action.

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This video series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!


Video Chapters:
0:00 What is a Power Series?
4:12 Examples of Power Series
9:22 Why & How Power Series Create Functions
12:28 Example of a Power Series Representing a Function
18:00 Important Notes/Facts About Power Series
19:09 Convergence & Radius of a Power Series (3 Ways)
22:17 Example - Power Series Convergent Only at x=c
30:46 Example - Power Series Convergent For all x
39:41 Example - Power Series Convergent Within a Radius R
53:21 Outro


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