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How to Use the Alternating Series Test & Approximate Sum of Alternating Series (Calculus 2 Lesson 27) In this video we learn how to determine if an alternating series converges or diverges by using the Alternating Series Test. An alternating series is a series whose terms alternate between being positive and negative. In order to converge, an alternating series must fail the divergence test and feature a sequence that is decreasing. When an alternating series converges, its sum can be approximated using a particular error formula. We take a look at several examples of using the Alternating Series Test, and an example of approximating the sum of a convergent alternating series. 🖥️ Join My Membership Site: https://www.jkmathematics.com/plus This video series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture! Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 What is an Alternating Series? 4:00 The Alternating Series Test 5:58 Why The Alternating Series Test Works (Visual) 9:50 Example - (-1)^n/n 14:24 Example - (-1)^n(2n+1)/(3n) 17:44 Example - 5(-1)^n/(2+n^3) 20:39 Example - (-1)^n/2^n 22:54 Example - n(-1)^n/ln(n) 25:40 Alternating Series Remainder / Error 32:37 Example - (-1)^n/n! (Part 1: Alternating Series Test) 35:08 Example - (-1)^n/n! (Part 2: Approximating the Sum) 40:51 Outro 📝 Examples Video: https://youtu.be/xXssfD_0ZRU ⏩ Next Lesson: https://youtu.be/52Gj0pJ2Iu0 📺 Calculus 2 Playlist: https://youtube.com/playlist?list=PLHdRLeAbIZE7KQ922piyRIDAj30XYcOIu 📺 Calculus 1 Playlist: https://youtube.com/playlist?list=PLHdRLeAbIZE6krGDQthaQRpLZFLD4ob54 🌐 Visit My Website: https://www.jkmathematics.com ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://amzn.to/3XuUcB9 Non-Graphing Calculator: https://amzn.to/46hHJ7E Financial Calculator: https://amzn.to/3CRe9s4 Graphing Paper: https://amzn.to/46mAfAr College Rule Paper: https://amzn.to/3NOJaTN My Favorite Pencil: https://amzn.to/3NOFMIB My Favorite Erasers: https://amzn.to/3PumUQB Calculus Workbook: https://amzn.to/3r8SnNP ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://amzn.to/3PzfI5F Calculus 3: https://amzn.to/46rSy76 Financial Mathematics: https://amzn.to/3ppIVW0 ⚡️My Recording Equipment⚡️ iPad Air: https://amzn.to/3phEug1 Apple Pencil (Gen 2): https://amzn.to/3Nl45MM Tablet Desk Stand: https://amzn.to/4420rPh External Hardrive: https://amzn.to/44pkEyh (Commissions earned on qualifying purchases) Find me on social media: Facebook: https://www.facebook.com/jkmathematics Twitter: https://twitter.com/jk_mathematics Instagram: @jk_mathematics Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! -Josh from JK Math #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.