Power Series - Representation of Functions - Calculus 2

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. Final Exam and Test Prep Videos: https://bit.ly/41WNmI9 _______________________________ Series Tests - Practice Problems: https://www.youtube.com/watch?v=0YeON4p0ogw Taylor & Maclaurin Polynomials: https://www.youtube.com/watch?v=urPIxvNBXF0 Taylor's Remainder Theorem: https://www.youtube.com/watch?v=lY0LzJXTgeo Power Series - Interval Convergence: https://www.youtube.com/watch?v=EGni2-m5yxM Power Series - Derivatives & Integrals: https://www.youtube.com/watch?v=nD6hai32ykQ ___________________________________ Power Series - Function Representation: https://www.youtube.com/watch?v=54yldObvvwY Finding The Power Series: https://www.youtube.com/watch?v=PmHaNjDBh_c Power Series - Representation By Integration: https://www.youtube.com/watch?v=0HyM3nM87mk Power Series - Representation By Natural Logs: https://www.youtube.com/watch?v=A6JdlY52NFg Taylor & Maclaurin Series: https://www.youtube.com/watch?v=LDBnS4c7YbA Binomial Series: https://www.youtube.com/watch?v=V1AKAkGJlN8 ____________________________________ Parametric Equations: https://www.youtube.com/watch?v=97pe-QlSGqA Calculus Final Exam and Video Playlists: https://www.video-tutor.net/ Full-Length Videos and Worksheets: https://www.patreon.com/MathScienceTutor/collections