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:

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 72E
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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)
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