Determine whether the following series converges. k E (- 1)k +1, 22k + 1 k=1 Select the correct answer below and, if necessary, fill in the answer box(es) to complete your choice. O A. The series converges because a = and for any index N, there are some values of k>N for which a12 a, and some values of k>N for which a.1 sa,. O B. The series converges by the Divergence Test because a, = and lim a, = k00 O C. The series converges because a, = is nondecreasing in magnitude for k greater than some index N. O D. The series diverges because a, = and for any index N, there are some values of k >N for which aa12 a, and some values of k> N for which a,, sa, O E. The series diverges because a = is nondecreasing in magnitude for k greater than some index N. OF. The series diverges by the Divergence Test because a = and lim a = k00
Determine whether the following series converges. k E (- 1)k +1, 22k + 1 k=1 Select the correct answer below and, if necessary, fill in the answer box(es) to complete your choice. O A. The series converges because a = and for any index N, there are some values of k>N for which a12 a, and some values of k>N for which a.1 sa,. O B. The series converges by the Divergence Test because a, = and lim a, = k00 O C. The series converges because a, = is nondecreasing in magnitude for k greater than some index N. O D. The series diverges because a, = and for any index N, there are some values of k >N for which aa12 a, and some values of k> N for which a,, sa, O E. The series diverges because a = is nondecreasing in magnitude for k greater than some index N. OF. The series diverges by the Divergence Test because a = and lim a = k00
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...
Related questions
Question
![Determine whether the following series converges.
k
Σ(-11.
22k + 1
k= 1
....
Select the correct answer below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The series converges because a, =
and for any index N, there are some values of k>N for which a,2 a, and some values of k>N for which a, sa,.
O B. The series converges by the Divergence Test because a, =
and lim a, =
k00
O C. The series converges because a
is nondecreasing in magnitude for k greater than some index N.
%3D
O D. The series diverges because a =
and for any index N, there are some values of k> N for which a,1z a, and some values of k >N for which a,1 sa,
O E. The series diverges because a
is nondecreasing in magnitude
k greater than some index N
OF. The series diverges by the Divergence Test because a, =
and lim a =
k00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbae19ae-fe97-42ad-a9d0-6a05eafe9580%2F72002a5e-c1b2-4936-b0ca-9cbced70c803%2Fz98ptr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Determine whether the following series converges.
k
Σ(-11.
22k + 1
k= 1
....
Select the correct answer below and, if necessary, fill in the answer box(es) to complete your choice.
O A. The series converges because a, =
and for any index N, there are some values of k>N for which a,2 a, and some values of k>N for which a, sa,.
O B. The series converges by the Divergence Test because a, =
and lim a, =
k00
O C. The series converges because a
is nondecreasing in magnitude for k greater than some index N.
%3D
O D. The series diverges because a =
and for any index N, there are some values of k> N for which a,1z a, and some values of k >N for which a,1 sa,
O E. The series diverges because a
is nondecreasing in magnitude
k greater than some index N
OF. The series diverges by the Divergence Test because a, =
and lim a =
k00
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