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How to Represent Functions as Maclaurin Series Using the Binomial Series (Calculus 2 Lesson 36) In this video we learn about the Binomial series and how to use it to represent functions of a certain form as a Maclaurin series. We first find the form of the Binomial series by representing the function (1+x)^k as a Maclaurin series, and discuss how to determine its interval of convergence. Then we look at examples of using the Binomial series to represent functions as a Maclaurin 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 Finding the Binomial Series 13:11 The Binomial Series 14:33 Interval of Convergence for Binomial Series 16:49 Example - f(x) = 1/(1+x)^2 25:10 Example - f(x) = sqrt(1+x) 41:36 Outro 📝 Examples Video: https://www.youtube.com/watch?v=u-PJUjpfLX0 ⏩ Next Lesson: https://www.youtube.com/watch?v=JlYS8lYwOPg 📺 Calculus 2 Playlist: https://www.youtube.com/playlist?list=PLHdRLeAbIZE7KQ922piyRIDAj30XYcOIu 📺 Calculus 1 Playlist: https://www.youtube.com/playlist?list=PLHdRLeAbIZE6krGDQthaQRpLZFLD4ob54 🌐 Visit My Website: https://www.jkmathematics.com ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://www.amazon.com/Texas-Instruments-TI-Nspire-Graphing-Calculator/dp/B07RL7HM5V?language=en_US Non-Graphing Calculator: https://www.amazon.com/Texas-Instruments-TI-30X-Scientific-Calculator/dp/B00SWWKEAY?language=en_US Financial Calculator: https://www.amazon.com/s?k=ba+2+plus&language=en_US Graphing Paper: https://www.amazon.com/KAISA-Punched-Loose-Leaf-Binders-150sheet/dp/B096V2RYR2?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&language=en_US College Rule Paper: https://www.amazon.com/Mead-Filler-College-Punched-15326/dp/B000068UWB?language=en_US My Favorite Pencil: https://www.amazon.com/Quick-Mechanical-Pencil-Assorted-Barrel/dp/B07FC5NGBX?language=en_US My Favorite Erasers: https://www.amazon.com/Prismacolor-Premier-Magic-Erasers-3-Count/dp/B005ENNEJW?language=en_US Calculus Workbook: https://www.amazon.com/Essential-Calculus-Practice-Workbook-Solutions/dp/1941691242?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&language=en_US ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://www.amazon.com/Calculus-Ron-Larson/dp/0547167024?language=en_US Calculus 3: https://www.amazon.com/Multivariable-Calculus-Ron-Larson/dp/1285060296?language=en_US Financial Mathematics: https://www.amazon.com/Mathematics-Investment-Credit-ACTEX-Academic/dp/1566987679?language=en_US ⚡️My Recording Equipment⚡️ iPad Air: https://www.amazon.com/Apple-iPad-Air-5th-Generation/dp/B09V3HJBN3?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1&language=en_US Apple Pencil (Gen 2): https://www.amazon.com/Apple-MU8F2AM-A-Pencil-Generation/dp/B07K1WWBJK?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&language=en_US Tablet Desk Stand: https://www.amazon.com/OMOTON-Adjustable-Multi-Angle-Aluminum-Convenient/dp/B015FH0XKE?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1&language=en_US External Hardrive: https://www.amazon.com/Toshiba-HDTB420XK3AA-Canvio-Portable-External/dp/B079D3D8NR?language=en_US (Commissions earned on qualifying purchases) Find me on social media: Facebook: https://www.facebook.com/unsupportedbrowser 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.