Determine whether the following series converges. Justify your answer. ∞ 5k +12k Σ 12k k=1 CL Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Type an exact answer.) A. The series is a geometric series with common ratio This is greater than 1, so the series diverges by the properties of a geometric series. OB. The limit of the terms of the series is so the series diverges by the Divergence Test. OC. The limit of the terms of the series does not exist, so the series diverges by the Divergence Test. D. The Root Test yields p= , so the series diverges by the Root Test. OE. The series is a geometric series with common ratio This is less than 1, so the series converges by the properties of a geometric series. OF. The limit of the terms of the series is 0, so the series converges by the Divergence Test.
Determine whether the following series converges. Justify your answer. ∞ 5k +12k Σ 12k k=1 CL Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Type an exact answer.) A. The series is a geometric series with common ratio This is greater than 1, so the series diverges by the properties of a geometric series. OB. The limit of the terms of the series is so the series diverges by the Divergence Test. OC. The limit of the terms of the series does not exist, so the series diverges by the Divergence Test. D. The Root Test yields p= , so the series diverges by the Root Test. OE. The series is a geometric series with common ratio This is less than 1, so the series converges by the properties of a geometric series. OF. The limit of the terms of the series is 0, so the series converges by the Divergence Test.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:Determine whether the following series converges. Justify your answer.
5k+12k
12k
Σ
k=1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
(Type an exact answer.)
OA. The series is a geometric series with common ratio This is greater than 1, so the series diverges by the properties of a geometric series.
OB. The limit of the terms of the series is so the series diverges by the Divergence Test.
OC. The limit of the terms of the series does not exist, so the series diverges by the Divergence Test.
OD. The Root Test yields p=
so the series diverges by the Root Test.
O E. The series is a geometric series with common ratio This is less than 1, so the series converges by the properties of a geometric series.
OF. The limit of the terms of the series is 0, so the series converges by the Divergence Test.
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