Calculus II: Power series (Radius and interval of convergence)

In this video we introduce the idea of a power series and talk about the notion of the radius and interval of convergence.

00:00 - Introduction
00:15 - Definition of a power series
02:45 - Radius/Interval of convergence
07:32 - Example 1
14:55 - Example 2
23:13 - Example 3
33:15 - Example 4
37:06 - Example 5

[MathforThought]

In example 2, I should have put 19<=x<=23 instead of 19<x<23 since the series DOES converge at the endpoints.

[PeterParker-wyzd]

In example, just before 40:00, you write |x+1| < 1, but the radius of convergence is in the form |x-a| < 1. Is it okay to still take the radius of convergence to be one when the sign is not negative? (Btw, thank you so much for these! They're saving my life :)

[jasonmantri]

cloudy, for example 4, any "reason" or clarification why 2x-1 needs to tend to zero (making x=1/2 and R=0)? (I understand the steps you did at the end, but if I were to explain to someone else you know...)