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
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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
Transcribed Image Text: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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