MAT136H1 Lecture Notes - Ratio Test

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MAT136H1 Full Course Notes
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Question #2 (medium): taylor series and its radius of convergence. Radius of convergence is determined using the ratio test | So any value of that makes the limit to be less than falls in the radius of convergence. Find the taylor series for ( ) centered at the given value of . Assume that f has a power series expansion. Since ( ) is centered at : ( ) ( ) this is the taylor series for f(x). Now to find the radius of convergence, put into the ratio test. and ( ) Therefore for all values of the series is convergence.

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