Find the radius of convergence of the power series 2n+ly" 2 9n (n+4) (You do NOT need to find the interval of convergence.) RADIUS OF CONVERGENCE:

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
Find the radius of convergence of the power series
2n+ly"
2 9n (n+4)
(You do NOT need to find the interval of convergence.)
RADIUS OF CONVERGENCE:
Transcribed Image Text:Find the radius of convergence of the power series 2n+ly" 2 9n (n+4) (You do NOT need to find the interval of convergence.) RADIUS OF CONVERGENCE:
Expert Solution
Step 1

Find the radius of convergence.

Given:
2n+1,n
Σ
n=09" (n+4)
Consider,
2n+1 xn
An
9" (n+4)
2n+1+lyn+l _ 2n+2,n+1
"n+1 9n+1(n+1+4) 9"+l(n+5)
Step 2

Apply ratio test.

'n+l <1
(i.e.) limn-0
| 2n+2„n+1
9n+ (n+5)
<1
2n+1yn
lim,
9" (n+4)
| 2n+2„n+1 _9"(n+4)
<1
lim,
п0
9n+1(n+5) 2n+l,n
(n+4|
2x
<1
lim n0 9
'n-
(n+5)
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning