dition Chapter 9.7, Problem 9E > Explanation Given information: OO а" The series is nVn3" Calculation: Consider the sequence as follows: ат — пупз" Provide the sequence an+1 as follows: ап+1 (n+1)Vn+13"1 Calculate the ratio as shown below. (n+1)+1+1 antl z а, 3 (n+1)Vn+13"+1 3(n+1) Vn+1 Find the radius of convergence and interval of convergence as shown below. The radius of convergence is the half of the width of the interval 3-3) 2 =3 Hence, the radius of convergence is 3. Provide the series for the interval as shown below. At 3 Σ (-3)" n/n3" OO (1)" -, hence, the series is a divergent series. n3/2 n=1 = 3 At (3)" Σ. OO OO 1 hence, the series is a divergent series. nvn3" n3/2 Hence, the interval of convergence is -3 < x < 3.
dition Chapter 9.7, Problem 9E > Explanation Given information: OO а" The series is nVn3" Calculation: Consider the sequence as follows: ат — пупз" Provide the sequence an+1 as follows: ап+1 (n+1)Vn+13"1 Calculate the ratio as shown below. (n+1)+1+1 antl z а, 3 (n+1)Vn+13"+1 3(n+1) Vn+1 Find the radius of convergence and interval of convergence as shown below. The radius of convergence is the half of the width of the interval 3-3) 2 =3 Hence, the radius of convergence is 3. Provide the series for the interval as shown below. At 3 Σ (-3)" n/n3" OO (1)" -, hence, the series is a divergent series. n3/2 n=1 = 3 At (3)" Σ. OO OO 1 hence, the series is a divergent series. nvn3" n3/2 Hence, the interval of convergence is -3 < x < 3.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
Related questions
Question
Textbook : University Calculus
Section 9.7, problem #9
In this problem we have to find the series interval of convergence. Which i found to be -3<x<3, then i went to check the endpoints to see if they are included and when plugging in -3 or 3 for x i found those series to be divergent like how it says on this website, but then the answer on the website and in the back of the book says that the endpoints are included. Why are the endpoints included if both series come out to be divergent when testing the endpoints?
Transcribed Image Text:dition
Chapter 9.7, Problem 9E >
Explanation
Given information:
OO
а"
The series is
nVn3"
Calculation:
Consider the sequence as follows:
ат —
пупз"
Provide the sequence an+1 as follows:
ап+1
(n+1)Vn+13"1
Calculate the ratio
as shown below.
(n+1)+1+1
antl
z
а,
3
(n+1)Vn+13"+1
3(n+1) Vn+1
Find the radius of convergence and interval of convergence as shown
below.
Transcribed Image Text:The radius of convergence is the half of the width of the interval
3-3)
2
=3
Hence, the radius of convergence is 3.
Provide the series for the interval as shown below.
At 3
Σ
(-3)"
n/n3"
OO
(1)"
-, hence, the series is a divergent series.
n3/2
n=1
= 3
At
(3)"
Σ.
OO
OO
1
hence, the series is a divergent series.
nvn3"
n3/2
Hence, the interval of convergence is -3 < x < 3.
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