For the following problem, select the answer that makes the correct conclusion AND uses a valid justification. The series ∞ O n=1 e O converges by the Alternating Series Test O -n n converges since diverges since converges since -n e-" e-n converges since n n e-n n e-n n 1 < for n ≥ 1 and en 1 - for n ≥ 1 and n 1 < for n ≥ 1 and n →0 as n→→∞ n=1 n=1 8 1 en n=1 1 == diverges n 1 converges n diverges

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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For the following problem, select the answer that makes the correct conclusion AND uses a valid justification.
The series
O
∞
O
n=1
O converges by the Alternating Series Test
O
-n
n
converges since
diverges since
converges since
converges since
-n
e-
e-n
n
n
e-n
n
e-n
n
S
1
en
1
> - for n ≥ 1 and
n
for n ≥ 1 and
n
1
< for n ≥ 1 and
→0 as n→→∞
8 1
en
n=1
n=1
8
1
== diverges
n=1
1
converges
n
diverges
Transcribed Image Text:For the following problem, select the answer that makes the correct conclusion AND uses a valid justification. The series O ∞ O n=1 O converges by the Alternating Series Test O -n n converges since diverges since converges since converges since -n e- e-n n n e-n n e-n n S 1 en 1 > - for n ≥ 1 and n for n ≥ 1 and n 1 < for n ≥ 1 and →0 as n→→∞ 8 1 en n=1 n=1 8 1 == diverges n=1 1 converges n diverges
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