Determine whether the following series converges absolutely, converges conditionally, or diverges. (-1) K+1 9 .8 Σ(-1)+1 ak = k=1 no Are the terms of the sequence yes 00 Let Tak denote Σ k=1 k=1 (-1)K+1 9 8 k 100 decreasing? What can be concluded from these results using the Alternating Series Test? OA. The series Σak must diverge. B. The series a must converge. C. The series a must converge. OD. The series Σak must diverge. O E. The Alternating Series Test is inconclusive. Does the series a converge? O A. no, because of properties of p-series B. yes, because of properties of p-series C. no, because of properties of geometric series D. no, because of the Divergence Test O E. yes, because of properties of geometric series
Determine whether the following series converges absolutely, converges conditionally, or diverges. (-1) K+1 9 .8 Σ(-1)+1 ak = k=1 no Are the terms of the sequence yes 00 Let Tak denote Σ k=1 k=1 (-1)K+1 9 8 k 100 decreasing? What can be concluded from these results using the Alternating Series Test? OA. The series Σak must diverge. B. The series a must converge. C. The series a must converge. OD. The series Σak must diverge. O E. The Alternating Series Test is inconclusive. Does the series a converge? O A. no, because of properties of p-series B. yes, because of properties of p-series C. no, because of properties of geometric series D. no, because of the Divergence Test O E. yes, because of properties of geometric series
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Determine whether the following series converges absolutely, converges conditionally, or diverges.
(-1) K+1
9
00
Σ(-1) +18
k=1
O no
V
a =
yes
Are the terms of the sequence
k=1
00
Let Tak denate Σ
k=1
8
−1)k+1
9
48
9
decreasing?
What can be concluded from these results using the Alternating Series Test?
OA. The series Σak must diverge.
OB. The series Σak must converge.
The series a must converge.
OD. The series a must diverge.
O E. The Alternating Series Test is inconclusive.
Does the series a converge?
O A. no, because of properties of p-series
O B. yes, because of properties of p-series
OC. no, because of properties of geometric series
O D. no, because of the Divergence Test
O E. yes, because of properties of geometric series
G
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