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# Combining power series Use the power series | Ch 9.2 - 31E ISBN: 9780321570567 2

## Solution for problem 31E Chapter 9.2

Calculus: Early Transcendentals | 1st Edition

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Problem 31E

Combining power series Use the power series representation to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.p(x)= 2x6 In (1 ? x)

Step-by-Step Solution:

Solution 31EStep 1:In this problem we have to find the power series of p(x) = (centered at ‘o’), and the interval of convergence of the new series.Given f(x) = ln(1-x) = - , for -1…………(1)Step 2: Given , p(x) = = 2, since from(1). = - , since Step 3: Now , we have to find out the interval of convergence of the new series. The new series is ; p(x) = -Use Ratio test to determine the interval of convergence.If and1. If L <1, converges.2. If L >1, diverges.3. If L=1, the test is inconclusive.

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##### ISBN: 9780321570567

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