Use Ratio Test to find Radius & Interval of Convergence

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Lesson 8.5 from Calculus Extended by J. Michael Shaw & Gary Taylor. This video covers how to use the Ratio Test to determine the Radius of Convergence and Interval of Convergence of a Power Series.
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I dont really understand the last bit, why is it usually in the form 1/R |x-c|

samlewis