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Determine whether the following series converges absolutely, converges conditionally, or diverges. [M8 9 cos k Σ 2k7 k=1 What can be concluded from these results using the Alternating Series Test? OA. The series Σak must converge. B. The series Σak must converge. OC. The series Σak must diverge. OD. The series |ak| must diverge. E. The Alternating Series Test does not apply to this series. Does the series ak| converge? A. yes, as can be determined by the Comparison Test, comparing against an appropriate p-series B. no, because of properties of p-series O C. yes, because of properties of p-series O D. no, because of the Divergence Test O E. yes, because of the Alternating Series Test Does the series Σak converge absolutely, converge conditionally, or diverge? O A. The series converges conditionally because Σ |ak| converges but Σak diverges. B. The series diverges because lim ak #0. k→∞o C. The series converges absolutely because a converges. D. The series diverges because a diverges. O E. The series converges conditionally because a converges but Σlak diverges.

Determine whether the following series converges absolutely, converges conditionally, or diverges. [M8 9 cos k Σ 2k7 k=1 What can be concluded from these results using the Alternating Series Test? OA. The series Σak must converge. B. The series Σak must converge. OC. The series Σak must diverge. OD. The series |ak| must diverge. E. The Alternating Series Test does not apply to this series. Does the series ak| converge? A. yes, as can be determined by the Comparison Test, comparing against an appropriate p-series B. no, because of properties of p-series O C. yes, because of properties of p-series O D. no, because of the Divergence Test O E. yes, because of the Alternating Series Test Does the series Σak converge absolutely, converge conditionally, or diverge? O A. The series converges conditionally because Σ |ak| converges but Σak diverges. B. The series diverges because lim ak #0. k→∞o C. The series converges absolutely because a converges. D. The series diverges because a diverges. O E. The series converges conditionally because a converges but Σlak diverges.

Advanced Engineering Mathematics
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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Determine whether the following series converges absolutely, converges conditionally, or diverges. Σ k=1 9 cos k 2k' What can be concluded from these results using the Alternating Series lest? O A. The series Σak must converge. OB. The seriesak must converge. OC. The series ak must diverge. OD. The series Σak must diverge. E. The Alternating Series Test does not apply to this series. Does the series ak converge? A. yes, as can be determined by the Comparison Test, comparing against an appropriate p-series OB. no, because of properties of p-series O C. yes, because of properties of p-series O D. no, because of the Divergence Test O E. yes, because of the Alternating Series Test Does the series ak converge absolutely, converge conditionally, or diverge? O A. The series converges conditionally because ➤ |ax| converges but a diverges. O B. The series diverges because lim ak #0. 00+X C. The series converges absolutely because Σ ak converges. OD. The series diverges because a diverges. O E. The series converges conditionally because Σak converges but Σlak diverges. (...)
Transcribed Image Text:Determine whether the following series converges absolutely, converges conditionally, or diverges. Σ k=1 9 cos k 2k' What can be concluded from these results using the Alternating Series lest? O A. The series Σak must converge. OB. The seriesak must converge. OC. The series ak must diverge. OD. The series Σak must diverge. E. The Alternating Series Test does not apply to this series. Does the series ak converge? A. yes, as can be determined by the Comparison Test, comparing against an appropriate p-series OB. no, because of properties of p-series O C. yes, because of properties of p-series O D. no, because of the Divergence Test O E. yes, because of the Alternating Series Test Does the series ak converge absolutely, converge conditionally, or diverge? O A. The series converges conditionally because ➤ |ax| converges but a diverges. O B. The series diverges because lim ak #0. 00+X C. The series converges absolutely because Σ ak converges. OD. The series diverges because a diverges. O E. The series converges conditionally because Σak converges but Σlak diverges. (...)
Determine whether the following series converges absolutely, converges conditionally, or diverges. Σ k=1 Find lim ak. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 9 cos k 2k² 00+x CA. lim a = 0 no 00+X OB. The limit does not exist. What can be concluded from this result using the Divergence Test? O A. The series Σak must diverge. OB. The series Σak | OC. The series Σak must converge. OD. The series a must converge. E. The Divergence Test is inconclusive. Are the terms of the sequence |ak| decreasing after some point? yes must diverge. What can be concluded from these results using the Alternating Series Test? O A. The series a must converge. OB. The seriesak must converge. OC. The series Σak must diverge. C
Transcribed Image Text:Determine whether the following series converges absolutely, converges conditionally, or diverges. Σ k=1 Find lim ak. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 9 cos k 2k² 00+x CA. lim a = 0 no 00+X OB. The limit does not exist. What can be concluded from this result using the Divergence Test? O A. The series Σak must diverge. OB. The series Σak | OC. The series Σak must converge. OD. The series a must converge. E. The Divergence Test is inconclusive. Are the terms of the sequence |ak| decreasing after some point? yes must diverge. What can be concluded from these results using the Alternating Series Test? O A. The series a must converge. OB. The seriesak must converge. OC. The series Σak must diverge. C
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