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Q. 3

Expert-verified

Found in: Page 669

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

What is a power series in x?

A power series in x is $\sum_{k = 0}^{\infty} a_{k} x^{k}$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

Consider the given question,

Step 2. Determine a power series in x.

If $\sum_{k = 0}^{\infty} a_{k}$ is a sequence of real numbers and x is a variable.

Then a power series in x is a series of the form $\sum_{k = 0}^{\infty} a_{k} x^{k}$ .

Rewriting the series,

$\sum_{k = 0}^{\infty} a_{k} x^{k} = a_{0} + a_{1} x + a_{2} x^{2} + . . .$

Most popular questions for Math Textbooks

In Exercises 49–56 find the Taylor series for the specified function and the given value of $x_{0}$ . Note: These are the same functions and values as in Exercises 41–48.

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Prove that if $(- p, p]$ is the interval of convergence for the series $\sum_{k = 0}^{\infty} a_{k} x^{k}$ , then the series converges conditionally at $p$ .

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In Exercises 23–32 we ask you to give Lagrange’s form for the corresponding remainder, $R_{4} (x)$

$\ln (1 + x)$

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What is a power series in x?

Step by Step Solution

Step 1. Given information.

Step 2. Determine a power series in x.

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What is a power series in x?

Step by Step Solution

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