   Chapter 11.8, Problem 41E

Chapter
Section
Textbook Problem

Suppose the series ∑ c n x n has radius of convergence 2 and the series ∑ d n x n has radius of convergence 3. What is the radius of convergence of the series ∑ ( c n + d n ) x n ?

To determine

To find:

The radius of convergence of the series cn+dnxn

Explanation

1) Concept:

For a power series n=0cnx-an, there is a positive number R such that the series converges if x-a<R and diverges if x-a>R, this number R is called the radius of convergence and the series is centered at x=a

2) Given:

The radius of convergence of the series cnxn is 2,  and radius of convergence of the series dnxn is 3

3) Calculation:

The radius of convergence of cnxn is  2, that is, this series converges for -2x2, and the radius of convergence of the series dnxn is 3, that is, this series converges for -3x3

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