Sequences and Series 4: Alternating series
15 videos • 9,133 views • by Jim Fowler Last week, in Week 3, we considered convergence tests; this week, we consider convergence for series with some negative and some positive terms. Up until now, we had been considering series with nonnegative terms; it is much easier to determine convergence when the terms are nonnegative. So this week, when we consider series with both negative and positive terms, there will definitely be some new complications. Specifically, we consider absolute and conditional convergence, alternating series and the alternating series test, as well as the limit comparison test. In a certain sense, this week is the end of our asking "Does it converge?" Next week, we consider power series and then, in Week 6, we consider Taylor series. Those last two topics will move us away from questions of mere convergence, so if you have been eager for new material, stay tuned. And if you have any questions or concerns about anything at all, I hope you will post a comment here, or write to me at fowler@math.osu.edu I am looking forward to hearing from you. Your feedback teaches me a ton about what works and what doesn't in this course, so I very much appreciate it!