Determine whether the following series converges. Justify your answer. 00 k Σ k = 1 Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. The limit of the terms is , so the series converges by the Divergence Test. O B. The terms of the series alternate in sign and their limit is so the series diverges by the Alternating Series Test. The Root Test yields p= lim Because p< 1, the series converges by the Root Test. k00 OD. The Root Test yields p= lim KIELT= Because p> 1, series diverges by the Root Test. k-00 O E. The Ratio Test yields r = This is greater than 1, so the series diverges by the Ratio Test.
Determine whether the following series converges. Justify your answer. 00 k Σ k = 1 Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) O A. The limit of the terms is , so the series converges by the Divergence Test. O B. The terms of the series alternate in sign and their limit is so the series diverges by the Alternating Series Test. The Root Test yields p= lim Because p< 1, the series converges by the Root Test. k00 OD. The Root Test yields p= lim KIELT= Because p> 1, series diverges by the Root Test. k-00 O E. The Ratio Test yields r = This is greater than 1, so the series diverges by the Ratio Test.
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.
k
k = 1
Select the correct choice below and fill in the answer box to complete your choice.
(Type an exact answer.)
O A. The limit of the terms is , so the series converges by the Divergence Test.
O B. The terms of the series alternate in sign and their limit is
so the series diverges by the Alternating Series Test.
O C.
The Root Test yields p= lim
Because p< 1, the series converges by the Root Test.
O D.
The Root Test yields p= lim
Because p> 1, series diverges by the Root Test.
k-00
O E. The Ratio Test yields r =
This is greater than 1, so the series diverges by the Ratio Test.
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