Determine whether the following series converge. Justify your answer. 29 29 29 29 2.3 4.5 6.7 8.9 + O E. Let ak = + Let ak = Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) OA. The Ratio Test yields r = . This is less than 1, so the series converges by the Ratio Test. OB. The limit of the terms of the series is so the series converges by the Divergence Test. OC. The Ratio Test yields r = This is greater than 1, so the series diverges by the Ratio Test. O D. ak bk + 29 4K² + 2k 29 + ... 4K + 2k =1/1 2 and bk = and bk = 1 K² Since lim k→∞ Since lim ak , bk k→∞ = G = the series converges by the Limit Comparison Test. the series diverges by the Limit Comparison Test.
Determine whether the following series converge. Justify your answer. 29 29 29 29 2.3 4.5 6.7 8.9 + O E. Let ak = + Let ak = Select the correct choice below and fill in the answer box to complete your choice. (Type an exact answer.) OA. The Ratio Test yields r = . This is less than 1, so the series converges by the Ratio Test. OB. The limit of the terms of the series is so the series converges by the Divergence Test. OC. The Ratio Test yields r = This is greater than 1, so the series diverges by the Ratio Test. O D. ak bk + 29 4K² + 2k 29 + ... 4K + 2k =1/1 2 and bk = and bk = 1 K² Since lim k→∞ Since lim ak , bk k→∞ = G = the series converges by the Limit Comparison Test. the series diverges by the Limit Comparison 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 converge. Justify your answer.
29 29 29 29
2.3 4.5
6.7 8.9
+
O E.
Let ak =
Select the correct choice below and fill in the answer box to complete your choice.
(Type an exact answer.)
OA. The Ratio Test yields r = . This is less than 1, so the series converges by the Ratio Test.
OB. The limit of the terms of the series is so the series converges by the Divergence Test.
This is greater than 1, so the series diverges by the Ratio Test.
OC. The Ratio Test yields r =
O D.
Let ak =
+
29
4K² + 2k
29
+ ...
4K + 2k
and bk =
and bk
=
1
k²
1
K²
Since lim
k→∞
Since lim
k→∞
ak
bk
ak
, bk
=
G
=
the series converges by the Limit Comparison Test.
the series diverges by the Limit Comparison Test.
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