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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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Series to functions Find the function represented by the

Chapter 8, Problem 52E

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QUESTION:

Series to functions Find the function represented by the following series and find the interval of convergence of the series.

\(\sum_{k=0}^{\infty}\left(x^{2}+1\right)^{2 k}\)

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QUESTION:

Series to functions Find the function represented by the following series and find the interval of convergence of the series.

\(\sum_{k=0}^{\infty}\left(x^{2}+1\right)^{2 k}\)

ANSWER:

Solution 52EStep 1:In this problem we have to find the function represented by the series and also we have to find the interval of convergence of the series . = 1+ +++................ Is an infinite geometric series and use the formula for a geometric series. That is , with |r| > 1Therefore , = , for || > 1 ( Since = , for | > 1) = , since +2ab+ = for || > 1 = for || > 1Thus the function represented by the power series is =

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