Determine whether the following series converges. Justify your answer. 23 (3) Σ tan k=1

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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Question
Determine whether the following series converges. Justify your answer.
k=1
OB.
8
O C.
O D.
tan
-1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A.
23
√k
Because
23
√k
Stan
-1
ak
Because L = lim -=
k→∞o k
(Type an exact answer.)
Because tan
ak
Because L = lim ==
k→∞o k
(Type an exact answer.)
23
√k
23
√k
∞
and Σοκ = Σ
k=1
S
∞
and Σbk = Σ
k=1
23
√k
8
23
and Wok = Σ converges, the given series converges by the Comparison Test.
√k
k=1
(...)
23
√k
23
√k
N
converges, the given series converges by the Limit Comparison Test.
diverges, the given series diverges by the Limit Comparison Test.
8
23
and Ebk = Σ diverges, the given series diverges by the Comparison Test.
√k
k=1
Transcribed Image Text:Determine whether the following series converges. Justify your answer. k=1 OB. 8 O C. O D. tan -1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. 23 √k Because 23 √k Stan -1 ak Because L = lim -= k→∞o k (Type an exact answer.) Because tan ak Because L = lim == k→∞o k (Type an exact answer.) 23 √k 23 √k ∞ and Σοκ = Σ k=1 S ∞ and Σbk = Σ k=1 23 √k 8 23 and Wok = Σ converges, the given series converges by the Comparison Test. √k k=1 (...) 23 √k 23 √k N converges, the given series converges by the Limit Comparison Test. diverges, the given series diverges by the Limit Comparison Test. 8 23 and Ebk = Σ diverges, the given series diverges by the Comparison Test. √k k=1
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