1 Vn? +4 Part 1: Start with the Divergence Test Write the corresponding positive terms: un = Evaluate the limit: lim un = Since lim u, is Select then the Divergence Test tells us Select 1 00 Part 2: Alternating Series Test d Compute the derivative: Un dn d Since dn Select the sequence Select So the Alternating Series Test tells us Select Part 3: Absolute Conv / Conditional Conv / Div (-1)"n² /n² + 4 Since the corresponding positive series Select v by Select then the alternating series Select n1 Vn? + 4
1 Vn? +4 Part 1: Start with the Divergence Test Write the corresponding positive terms: un = Evaluate the limit: lim un = Since lim u, is Select then the Divergence Test tells us Select 1 00 Part 2: Alternating Series Test d Compute the derivative: Un dn d Since dn Select the sequence Select So the Alternating Series Test tells us Select Part 3: Absolute Conv / Conditional Conv / Div (-1)"n² /n² + 4 Since the corresponding positive series Select v by Select then the alternating series Select n1 Vn? + 4
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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Test the series for convergence or divergence.
∑n=1∞(−1)nn3n7+4−−−−−√.∑n=1∞(−1)nn3n7+4.
Part 1: Start with the Divergence 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
Since the corresponding positive series ∑n=1∞n3n7+4−−−−−√∑n=1∞n3n7+4 by , then the alternating series ∑n=1∞(−1)nn3n7+4−−−−−√∑n=1∞(−1)nn3n7+4
Transcribed Image Text:* (-1)*n²
n=1 yn? +4
Part 1: Start with the Divergence Test
Write the corresponding positive terms: u, =
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:
"n.
dn
d
Un Select
dn
Since
the sequence Select
So the Alternating Series Test tells us Select
Part 3: Absolute Conv / Conditional Conv / Div
(-1)"n³
Since the corresponding positive series -"
Select
v by Select
then the alternating series
Select
n=1 Vn? + 4
n-1 Vn7 + 4
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