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๐Ÿ‘‘ย  Unit 1: Limits & Continuity

๐Ÿถย  Unit 8: Applications of Integration

โ™พย  Unit 10: Infinite Sequences and Series (BC Only)

10.13 Radius and Interval of Convergence of Power Series

#convergence

#powerseries

#radius

#interval

โฑ๏ธย ย 1 min read

written by

Peter Cao

peter cao


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One of the questions we have about power series approximations of functions is where the approximation is valid, or in other words, where the power series converges. For a given x, we can find the radius, and then the interval of convergence for a power series.

For a Taylor series centered at x = a, the only place where we are sure that it converges for now is x = a, but we can expand this to a greater range using our knowledge of the ratio test. Letโ€™s make an example to demonstrate this!

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We have to test the endpoints by plugging them into x as sometimes it may converge or diverge at the endpoints.

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Problems

Find the interval, radius of convergence, and the center of the interval of convergence.

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