Sequences and Series 5: Power series
14 videos • 15,180 views • by Jim Fowler Last week, in Week 4, we considered alternating series and the limit comparison test; this week, we will consider power series. Up until now, we had been considering series one at a time; with power series, we are considering a whole family of series, namely sum_{n=0}^infinity a_n x^n, which depend on a parameter x. They are like polynomials, so they are easy to work with. And yet, lots of functions we care about, like e^x, can be represented as power series, so power series bring the relaxed atmosphere of polynomials to the harder realm of functions like e^x. And we are almost done! Next week, in Week 6, we wrap up the course with Taylor series, which are really a special case of power series. So if you fall in love with power series, there is more to come. And if you don't like power series, well, there isn't much left! Either way, hang in there. If you have any questions or concerns about anything at all, I hope you will post a question here, or write to me at fowler@math.osu.edu. I really enjoy being able to chat with you.