In our previous lesson on Power Series, we focused on finding the Radius and Interval of Convergence.
Now, it’s time to look at how to represent certain types of Functions as Sums of Power Series, or Power Series Representation.
How can we do this?
Power Series Expansion Formula
Well, there is an amazing connection between a Power Series and the Geometric Series.
We start with knowing that a Geometric Series will converge as long as the common ratio is between -1 and 1. And if so, then we have a formula that enables us to find the Sum of that infinite geometric Series.
Well, this formula is going to be the key, or basic form, for how we can represent functions as an infinite series!
Sometimes, the Power Series Expansion will be quick, and sometimes we will have to use our knowledge of Partial Fractions, Differentiation or even Integration to create the sum of a power series.
Don’t worry, it will become very clear as to when you will need to use what is called term-by-term differentiation and integration, as Oregon State accurately states, and the overall process is really quite simple.
Together we will look at 15 examples in great detail, so you will feel confident in how to find a power series representation for a function!
Power Series Representation – Video
Get access to all the courses and over 450 HD videos with your subscription
Monthly and Yearly Plans Available
Still wondering if CalcWorkshop is right for you?
Take a Tour and find out how a membership can take the struggle out of learning math.