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Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 5.1 - Problem 5
Get Full Access to Elementary Differential Equations And Boundary Value Problems - 10 Edition - Chapter 5.1 - Problem 5

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# Solution: In each of 1 through 8, determine the radius of convergence of the given power

ISBN: 9780470458310 168

## Solution for problem 5 Chapter 5.1

Elementary Differential Equations and Boundary Value Problems | 10th Edition

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Problem 5

In each of 1 through 8, determine the radius of convergence of the given power series.n=1(2x + 1)nn2

Step-by-Step Solution:
Step 1 of 3

1.3​ ​Solving​ ​Equations Definition:​ ​two​ ​equations​ ​are​ ​​equivalent​ ​​if​ ​they​ ​share​ ​the​ ​same​ ​solutions. Definition:​ ​a,​ ​b,​ ​c​​ ​​∈​​ ​R 1. a​ ​=​ ​b​ i​ s​ ​​Equivalent​ ​​to​ ​a​ ​+​ ​c​ ​=​ ​b​ ​+​ ​c 2. a​ ​=​ ​b​ ​​ quivalent​ ​t ​ o​ ​ac​ ​=​ ​b​ c≠0) Example:​ ​y​ ​+​ ​4.3​ ​=​ ​11.2→​ ​y​ ​=​ ​11.2​ ​-​ ​4.3​ ​→​ ​ ​y​ ​=​ ​6.9 Definition:​ ​​Linear​ ​Equation:​​ ​​ ​​ ​T ​ ypes​ o ​ f​ ​Solutions: 1.​ ​​ ​​ ​​ ​​ ​​ ​Solution​ ​set​ i​ s​ ​R,​ ​identity Example:​ ​2x​ ​+​ ​2​ → ​ ​ ​0​ ​=​ ​0 2.​ ​​ ​​​ olution​ s ​ et​ ​is​​ ​,​ ​contradiction Example:​ ​x​ + ​ ​​ ​ ​=​ ​​ ​ ​3​ ​​ ​x​ ​=​ ​ ​ ​→​ ​0​ ​=​ ​1 3.​ ​​ ​​​ nique​ ​solution,​ ​c

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Step 3 of 3

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Solution: In each of 1 through 8, determine the radius of convergence of the given power