Power Series - Radius & Interval of Convergence - Calculus 2

A power series is a special type of series that involves a variable, usually x, raised to some power of n. As such, each of the terms of a power series involve x, and as a result, form a function f(x). However, this function is not any normal function, it is a function that is only defined for the values of x for which the power series is convergent. These values of x make up what is known as the interval of convergence for a power series.

The interval of convergence for a power series will be centered around a value c which is called "the center" of the power series. The endpoints of the interval will both be the same distance alway from the center, which is known as the radius of convergence. The focus of this lesson will be to establish the relationship between the convergence of a power series, and the function it represents, as well as how to find the radius and interval of convergence for a given power series. There's a lot to cover here, so let's get into it!

 In this lesson, you will learn:

• The form of a Power Series and how to identify one
• How a power series represents a function 
• How to find the radius and interval of convergence for a power series

I hope you find this video to be helpful!

-Josh