This is the first of two lessons on Power Series.
A Power Series is a function of x, and it is different from any other kind of series that we’ve looked at to this point.
Power Series Summation Formula
In all the previous videos we’ve only allowed numbers in the series, and now we are going to allow variables to be in the series as well.
Don’t worry.
This will not change how things work for how we find the convergence of a series because everything that we know about series still holds.
But we must keep in mind, that the convergence of a Power Series will now depend upon the values of x that we put into the series.
Interval of Convergence for a Power Series
In other words, according to Paul’s Online Notes, a power series may converge for some values of x and not for other values of x.
So in this lesson, we are going to focus on determining the Radius and Interval of Convergence for a function.
Which means we want to know for what values of x will our function converge (work)?
I’m confident that you will find this process to be extremely straightforward, after walking through our six examples where we will see we will need to make use of our ever popular Ratio and Root Tests.
Radius of Convergence – Video
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