Determine whether the following series converges absolutely, converges conditionally, or diverges. 00 (-1)kk5 Σ 12 k=1 √k +9 Does the series Σak converge absolutely, converge conditionally, or diverge? A. The series converges absolutely because Σak converges. B. The series converges conditionally because Σ |ak| converges but Σ a diverges. C. The series converges conditionally because Σ a converges but Σ |ak| diverges. OD. The series diverges because Σ |ak| diverges. E. The series diverges because lim ak #0. k→∞0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Determine whether the following series converges absolutely, converges conditionally, or
diverges.
(-1)kk5
00
Σ
12
k=1 √k
+9
...
Does the series Σak converge absolutely, converge conditionally, or diverge?
A. The series converges absolutely because Σak converges.
B. The series converges conditionally because Σ |ak| converges but Σ ak diverges.
OC. The series converges conditionally because Σ ak converges but Σ |ak| diverges.
D. The series diverges because Σak diverges.
E. The series diverges because lim ak * 0.
k→∞0
Transcribed Image Text:Determine whether the following series converges absolutely, converges conditionally, or diverges. (-1)kk5 00 Σ 12 k=1 √k +9 ... Does the series Σak converge absolutely, converge conditionally, or diverge? A. The series converges absolutely because Σak converges. B. The series converges conditionally because Σ |ak| converges but Σ ak diverges. OC. The series converges conditionally because Σ ak converges but Σ |ak| diverges. D. The series diverges because Σak diverges. E. The series diverges because lim ak * 0. k→∞0
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