   Chapter 11.8, Problem 32E

Chapter
Section
Textbook Problem

# Let p and q be real numbers with p < q. Find a power series whose interval of convergence is (a) (p, q) (b) (p, q] (c) [p, q) (d) [p, q]

(a)

To determine

To find: The power series whose interval of convergence is (p,q).

Explanation

The given interval of convergence is (p,q).

The midpoint of the interval is m=p+q2.

The radius of convergence is r=qp2.

Its known that the power series n=0xn has interval of convergence is (1,1).

Since the given interval is (p,q), both the radius of convergence and the midpoint must be shifted.

Change xn to (xr)n that shifts the radius of convergence

(b)

To determine

To find: The power series whose interval of convergence is (p,q].

(c)

To determine

To find: The power series whose interval of convergence is [p,q).

(d)

To determine

To find: The power series whose interval of convergence is [p,q].

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Expand each expression in Exercises 122. (2y+3)(y+5)

Finite Mathematics and Applied Calculus (MindTap Course List)

#### If 13f(x)dx=10 and 13g(x)dx=6, then 13(2f(x)3g(x))dx= a) 2 b) 4 c) 18 d) 38

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Self Check Factor: 8a3+1000b6.

College Algebra (MindTap Course List) 