Take a look at this video to see how a couple of warm-up problems on geometric series form the basis for our entire lesson on power series. Duration: 4:39

Building on our conclusions from the second warm-up exercise, we formally define a power series as essentially an infinitely long polynomial. That never-ending polynomial and then be defined as a function, whose domain is the set of numbers for which the sum of the polynomial terms converges. That domain is called the interval of convergence for the power function, and finding it is one of the things the AP exam will expect of us. Duration: 9:36

We begin this next video with a reexamination of the Ratio Test. Why? Well, that's the test we will use to find the interval of convergence for a power series. Since the Ratio Test is (clinically) the most satisfying of all the convergence tests, this is probably the most fun you can have with series. Oh, yeah, you'll also need some crayons. Duration: 15:44

Apparently, it is possible for a power series to converge only at its center point or over some finite and symmetric interval surrounding the center. There is one more possibility, as Example 3 demonstrates. Duration: 7:47

As the three previous problems demonstrated, the interval of convergence can take on exactly one of 3 different forms, and those intervals will have a radius of convergence of 0, L (some finite number), or ∞ respectively. For the finite case, remember to check your endpoints, as the power series may or may not converge there. Probably worth a point on the AP exam. Duration: 5:27

Finally, Example 5 presents us with three power series. If you've stayed awake this long, you probably know what to do here. Duration: 17:42