To test this series for convergence6+66"00n=1You could use the Limit Comparison Test, comparing it to the series where rCompleting the test, it shows the series:DivergesO ConvergesWe want to use the Alternating Series Test to determine if the series:XDk-4(−1)k+2_n-1¹2+10converges or diverges.We can conclude that:O The series converges by the Alternating Series Test.The Alternating Series Test does not apply because the absolute value of the terms are notdecreasing.sin n² ( 4 )kXThe Alternating Series Test does not apply because the absolute value of the terms do not approach0, and the series diverges for the same reason.The series diverges by the Alternating Series Test.O The Alternating Series Test does not apply because the terms of the series do not alternate.We want to use the Alternating Series Test to determine if the series:COSC² (+))converges or diverges.We can conclude that:O The series converges by the Alternating Series Test.The Alternating Series Test does not apply because the absolute value of the terms are notdecreasing.O The series diverges by the Alternating Series Test.The Alternating Series Test does not apply because the terms of the series do not alternate.The Alternating Series Test does not apply because the absolute value of the terms do not approach

Explanation of the answer is as follows

Answered: To test this series for convergence 6+6…

To test this series for convergence 6+6 6" n-1 You could use the Limit Comparison Test, comparing it to the series where r 2 Completing the test, it shows the series: ⒸDiverges O Converges X

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

To test this series for convergence
6+6
6"
00
n=1
You could use the Limit Comparison Test, comparing it to the series where r
Completing the test, it shows the series:
Diverges
O Converges
We want to use the Alternating Series Test to determine if the series:
XD
k-4
(−1)k+2_
n-1
¹2+10
converges or diverges.
We can conclude that:
O The series converges by the Alternating Series Test.
The Alternating Series Test does not apply because the absolute value of the terms are not
decreasing.
sin n² ( 4 )
k
X
The Alternating Series Test does not apply because the absolute value of the terms do not approach
0, and the series diverges for the same reason.
The series diverges by the Alternating Series Test.
O The Alternating Series Test does not apply because the terms of the series do not alternate.
We want to use the Alternating Series Test to determine if the series:
COS
C² (+))
converges or diverges.
We can conclude that:
O The series converges by the Alternating Series Test.
The Alternating Series Test does not apply because the absolute value of the terms are not
decreasing.
O The series diverges by the Alternating Series Test.
The Alternating Series Test does not apply because the terms of the series do not alternate.
The Alternating Series Test does not apply because the absolute value of the terms do not approach

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