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Alternating Series Test amp Remainder Calculus 2 Lesson 27 JK Math
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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: • Alternating Series Test Remainder E... • ⏩ Next Lesson: • Absolute Conditional Convergence | ... • 📺 Calculus 2 Playlist: • Calculus 2 • 📺 Calculus 1 Playlist: • Calculus 1 • • 🌐 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: / jkmathematics • Twitter: / 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.
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