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Tutorial Exercise Find the interval of convergence of the power series Be sure to include...

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Calculus

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Tutorial Exercise Find the interval of convergence of the power series Be sure to include a check for convergence at the endpoints of the interval 9x 1 Step 1 n 17 1 Recall the Ratio Test which states that ifa is a series with nonzero terms and lim n 81 For any fixed value of x such that x 0 let a 9x n 1 n 1 Then lim 818 an 1 an lim 318 lim 81B n 1 9x n 2 n 9x 1 n 1 n 1 9x n 2 n 1 a n 1 1 then a converges absolutely If lim n 318 a n P a n n 1 1 or lim 318 a n 1 a n then a diverges n

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