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# Solution: Combining power series Use the power series ISBN: 9780321570567 2

## Solution for problem 30E Chapter 9.2

Calculus: Early Transcendentals | 1st Edition

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Problem 30E

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.

f(x3) = In (1 − x3)

Step-by-Step Solution:

Solution 30EStep 1:

Given Using the power series representation for , we get Step 2:

Series is and To determine the radius of convergence we use ratio test which states: The ratio test states that:a. If then the series convergesb. If then the series divergesc. If or the limit does not exist then the test is inconclusive.

Calculating L, we get   For the series to be convergent So, the radius of convergence is 1.

Step 3 of 3

##### ISBN: 9780321570567

Since the solution to 30E from 9.2 chapter was answered, more than 237 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. The answer to “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.f(x3) = In (1 ? x3)” is broken down into a number of easy to follow steps, and 34 words. The full step-by-step solution to problem: 30E from chapter: 9.2 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: Series, power, interval, Find, functions. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

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