Use a convergence test of your choice to determine whether the following series converges or diverges. 00 4 Σ + 4 k= 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The Ratio Test yields r= This is less than 1, so the series converges by the Ratio Test. (Type an exact answer.) O B. The Ratio Test yields r= This is greater than 1, so the series diverges by the Ratio Test. (Type an exact answer.) OC. 00 4 4 is k +4 k 4 Because and converges, the given series converges by the Comparison Test. k=1 OD. 4 Because 00 4 4 k +4 k -2 and diverges, the given series diverges by the Comparison Test. k=1

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
Use a convergence test of your choice to determine whether the following series converges or diverges.
00
Σ
+4
k = 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The Ratio Test yields r=
This is less than 1, so the series converges by the Ratio Test. (Type an exact answer.)
O B. The Ratio Test yields r=
This is greater than 1, so the series diverges by the Ratio Test. (Type an exact answer.)
C.
4
Because
4
and
k
4
converges, the given series converges by the Comparison Test.
+4
k= 1
OD.
4.
Because
00
4
4
k +4 k
and E
diverges, the given series diverges by the Comparison Test.
k= 1
2°C
Cloudy
Transcribed Image Text:Use a convergence test of your choice to determine whether the following series converges or diverges. 00 Σ +4 k = 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The Ratio Test yields r= This is less than 1, so the series converges by the Ratio Test. (Type an exact answer.) O B. The Ratio Test yields r= This is greater than 1, so the series diverges by the Ratio Test. (Type an exact answer.) C. 4 Because 4 and k 4 converges, the given series converges by the Comparison Test. +4 k= 1 OD. 4. Because 00 4 4 k +4 k and E diverges, the given series diverges by the Comparison Test. k= 1 2°C Cloudy
Expert Solution
steps

Step by step

Solved in 2 steps with 1 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