Power Series - Radius & Interval of Convergence | Calculus 2 Lesson 31 - JK Math

How to Find the Radius & Interval of Convergence for Power Series (Calculus 2 Lesson 31) In this video we learn about Power Series and how to find their radius and interval of convergence. A power series is a type of series that includes a variable, such as x, raised to a power of n. Because of this included variable, the terms of a power series form a function. This function is only defined for the values of x that make the power series convergent. In order to find these values of x that make the power series convergent (interval of convergence), we will use many of the convergence tests and skills related to series that have been covered up to this point. We discuss how this is will be done, and go over a couple examples explaining and showing the process in action. 🖥️ 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 a Power Series? 4:12 Examples of Power Series 9:22 Why & How Power Series Create Functions 12:28 Example of a Power Series Representing a Function 18:00 Important Notes/Facts About Power Series 19:09 Convergence & Radius of a Power Series (3 Ways) 22:17 Example - Power Series Convergent Only at x=c 30:46 Example - Power Series Convergent For all x 39:41 Example - Power Series Convergent Within a Radius R 53:21 Outro 📝 Examples Video: https://youtu.be/uTTK8qLFPI8 ⏩ Next Lesson: https://youtu.be/jloA_OtzG-I 📺 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.