Binomial Series | Calculus 2 Lesson 36 - JK Math

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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.

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

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