   Chapter 9.9, Problem 32E Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Approximating a Sum In Exercises 31 and 32, (a) use a graphing utility to graph several partial sums of the series. b) find the sum of the series and its radius of convergence,(c) use a graphing utility and 50 terms of the series to approximate the sum when x = 0.5 . and (d) determine what the approximation represents and how good the approximation is. ∑ n = 0 ∞ ( − 1 ) n x 2 n + 1 ( 2 n + 1 ) !

(a)

To determine

To graph: The several partial sums of the series n=0(1)nx2n+1(2n+1)! by the use of a graphing utility.

Explanation

Given:

The series is,

n=0(1)nx2n+1(2n+1)!

Graph:

Let the two different series be n=010(1)nx2n+1(2n+1)! and n=015(1)nx2n+1(2n+1)!

(b)

To determine

To calculate: The sum of the series n=0(1)nx2n+1(2n+1)! and its radius of convergence.

(c)

To determine
The sum of the 50 terms of the series n=0(1)nx2n+1(2n+1)! when x=0.5 by the use of graphing utility.

(d)

To determine
What the approximation of the sum of the 50 terms of the series n=0(1)nx2n+1(2n+1)! when x=0.5 represent and also find the accuracy of the approximation.

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