Σ (-1)n+1 5n In(6n) n=3 Part 1: Start with the Divergence (n-th term) Test Write the corresponding positive terms: Un =| Evaluate the limit: lim um Since lim u, is Select then the Divergence Test tells us Select Part 2: Alternating Series Test d Un = dn Compute the derivative: d Since - Un Select the sequence Select dn So the Alternating Series Test tells us Select Part 3: Absolute Conv / Conditional Conv / Div Therefore from Part 1 and Part 2, the alternating series (-1)"+1 m(0n) 5n Select > >
Σ (-1)n+1 5n In(6n) n=3 Part 1: Start with the Divergence (n-th term) Test Write the corresponding positive terms: Un =| Evaluate the limit: lim um Since lim u, is Select then the Divergence Test tells us Select Part 2: Alternating Series Test d Un = dn Compute the derivative: d Since - Un Select the sequence Select dn So the Alternating Series Test tells us Select Part 3: Absolute Conv / Conditional Conv / Div Therefore from Part 1 and Part 2, the alternating series (-1)"+1 m(0n) 5n Select > >
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
Test the series for convergence or divergence.
∑n=3∞(−1)n+1ln(6n)5n.∑n=3∞(−1)n+1ln(6n)5n.
Part 1: Start with the Divergence (n-th term) Test
Write the corresponding positive terms: un=un=
Evaluate the limit: limn→∞un=limn→∞un=
Since limn→∞unlimn→∞un is , then the Divergence Test tells us .
Part 2: Alternating Series Test
Compute the derivative: ddnun=ddnun=
Since ddnunddnun , the sequence .
So the Alternating Series Test tells us
Part 3: Absolute Conv / Conditional Conv / Div
Therefore from Part 1 and Part 2, the alternating series ∑n=3∞(−1)n+1ln(6n)5n∑n=3∞(−1)n+1ln(6n)5n
Transcribed Image Text:(-1)n+1 In(6n)
5n
00
n=3
Part 1: Start with the Divergence (n-th term) Test
Write the corresponding positive terms: , =|
Evaluate the limit: lim u, =
Since lim u, is Select
then the Divergence Test tells us Select
Part 2: Alternating Series Test
d
Compute the derivative:
Un =
dn
d.
Since
-un-
Select
the sequence
Select
dn
So the Alternating Series Test tells us Select
Part 3: Absolute Conv / Conditional Conv / Div
In(6n)
Therefore from Part 1 and Part 2, the alternating series > (-1)"+1.
Select
5n
n=3
>
>
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