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This calculus 2 video tutorial provides a basic introduction into the representation of functions as power series. It explains how to represent a function as a power series centered at 0 and centered at some value c. It also explains how to approximate function values using geometric power series. This video also explains how to find the radius of convergence and the interval of convergence of a geometric power series. To write a power series from a function, you need to write the function in the form of the formula for the infinite sum of a geometric series. To find the interval of convergence, find the common ratio represented by some variable expression of x and set it less than 1 and solve the inequality. This video also includes examples and practice problems of adding and subtracting power series as well as using partial fraction decomposition.

Series Tests - Practice Problems:


Taylor & Maclaurin Polynomials:


Taylor's Remainder Theorem:


Power Series - Interval Convergence:


Power Series - Derivatives & Integrals:


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Power Series - Function Representation:


Finding The Power Series:


Power Series - Representation By Integration:


Power Series - Representation By Natural Logs:


Taylor & Maclaurin Series:


Binomial Series:


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Parametric Equations:


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