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Determine whether the following series converges. Justify your answer. 9 Σ (COST-COS 15) k+4 k+5 k=1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) O A. By the Telescoping Series Test, the limit of the terms of the sum does not exist. So, the series diverges by the Telescoping Series Test. OB. By the Telescoping Series Test, the limit of the terms of the sum is So, the series converges by the Telescoping Series Test. OC. The terms of the series are alternating and their limit does not exist, so the series diverges by the Alternating Series Test. 9 9 9 18

Determine whether the following series converges. Justify your answer. 9 Σ (COST-COS 15) k+4 k+5 k=1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) O A. By the Telescoping Series Test, the limit of the terms of the sum does not exist. So, the series diverges by the Telescoping Series Test. OB. By the Telescoping Series Test, the limit of the terms of the sum is So, the series converges by the Telescoping Series Test. OC. The terms of the series are alternating and their limit does not exist, so the series diverges by the Alternating Series Test. 9 9 9 18

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. Justify your answer. 9 Σ (CO-CO₂) Σcos- k+4 k +5 k=1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) O A. By the Telescoping Series Test, the limit of the terms of the sum does not exist. So, the series diverges by the Telescoping Series Test. B. By the Telescoping Series Test, the limit of the terms of the sum is. So, the series converges by the Telescoping Series Test. O C. The terms of the series are alternating and their limit does not exist, so the series diverges by the Alternating Series Test. O D. Because cos 9 9 9 cos- > cos k+5 9 k 00 for any positive integer k, and cos diverges, the given series diverges by the Comparison Test. k k=1 O E. The terms of the series are alternating and their limit is so the series converges by the Alternating Series Test.
Transcribed Image Text:Determine whether the following series converges. Justify your answer. 9 Σ (CO-CO₂) Σcos- k+4 k +5 k=1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an exact answer.) O A. By the Telescoping Series Test, the limit of the terms of the sum does not exist. So, the series diverges by the Telescoping Series Test. B. By the Telescoping Series Test, the limit of the terms of the sum is. So, the series converges by the Telescoping Series Test. O C. The terms of the series are alternating and their limit does not exist, so the series diverges by the Alternating Series Test. O D. Because cos 9 9 9 cos- > cos k+5 9 k 00 for any positive integer k, and cos diverges, the given series diverges by the Comparison Test. k k=1 O E. The terms of the series are alternating and their limit is so the series converges by the Alternating Series Test.
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