Determine whether the following series converges. Justify your answer. 00 k=1 +7 4 Select the correct choice below and fill in the answer box to complete your choice. k OA. The series is a geometric series with common ratio (Type an exact answer.) OC. OB. The Ratio Test yields r= (Type an exact answer.) D. Because k Because S +7 S for any positive integer k and converges, the given series converges by the Comparison Test. 4 4 +7 This is greater than 1, so the series diverges by the properties of a geometric series. This is less than 1, so the series converges by the Ratio Test. ****** OE. The series is a geometric series with common ratio (Type an exact answer.) k=1 k - for any positive integer k and Σ k=1 k diverges, the given series diverges by the Comparison Test. This is less than 1, so the series diverges by the properties of a geometric series.
Determine whether the following series converges. Justify your answer. 00 k=1 +7 4 Select the correct choice below and fill in the answer box to complete your choice. k OA. The series is a geometric series with common ratio (Type an exact answer.) OC. OB. The Ratio Test yields r= (Type an exact answer.) D. Because k Because S +7 S for any positive integer k and converges, the given series converges by the Comparison Test. 4 4 +7 This is greater than 1, so the series diverges by the properties of a geometric series. This is less than 1, so the series converges by the Ratio Test. ****** OE. The series is a geometric series with common ratio (Type an exact answer.) k=1 k - for any positive integer k and Σ k=1 k diverges, the given series diverges by the Comparison Test. This is less than 1, so the series diverges by the properties of a geometric series.
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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Transcribed Image Text:Determine whether the following series converges. Justify your answer.
00
k=1
+7
Select the correct choice below and fill in the answer box to complete your choice.
4
k
OA. The series is a geometric series with common ratio
(Type an exact answer.)
OC.
OB. The Ratio Test yields r=
(Type an exact answer.)
D.
Because
Because
k
S
+7
S for any positive integer k and converges, the given series converges by the Comparison Test.
4
4 +7
This is greater than 1, so the series diverges by the properties of a geometric series.
This is less than 1, so the series converges by the Ratio Test.
*** ***
O E. The series is a geometric series with common ratio
(Type an exact answer.)
k=1 k
- for any positive integer k and Σ
k=1 k
diverges, the given series diverges by the Comparison Test.
This is less than 1, so the series diverges by the properties of a geometric series.
WD
Time Re
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