Determine whether 3" is convergent. Specifically, use the Comparison Test to compare this 2n+9./ñ series to a geometric series. * 3" is convergent (please answer true or false). | 22n+9./ñ Claim: The common ratio of the geometric series suitable for applying the Comparison Test is r = Claim: b, 3" and an = r" satisfy 22n+9.Vñ (1) 0 < an < bn for all large n > 1 or (2) 0 < bn < an for all large n > 1) onter (1) or (2)
Determine whether 3" is convergent. Specifically, use the Comparison Test to compare this 2n+9./ñ series to a geometric series. * 3" is convergent (please answer true or false). | 22n+9./ñ Claim: The common ratio of the geometric series suitable for applying the Comparison Test is r = Claim: b, 3" and an = r" satisfy 22n+9.Vñ (1) 0 < an < bn for all large n > 1 or (2) 0 < bn < an for all large n > 1) onter (1) or (2)
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:3n
Determine whether
is convergent. Specifically, use the Comparison Test to compare this
22n+9.Vn
n=1
series to a geometric series.
3n
Claim:
is convergent (please answer true or false). |
22n+9./ñ
n=1
The common ratio of the geometric series suitable for applying the Comparison Test is r =
3n
Claim: b,
and an = r" satisfy
22n+9.Vn
(1) 0 < an < bn for all large n >lor
(2) 0 < bn < an for all large n > 1)
(please enter (1) or (2)).
n2 + 5
Determine whether the series
is convergent using the Comparison Test to compare it to a p-
n² In n
n=2
series.
Hint: Recall that 0 < Inn < n for n > 2.
n2 + 5
Claim:
is convergent (please answer true or false). |
n2 Inn
n=2
The parameter of the p-series suitable for applying the Comparison Test is p
n² + 5
1
Claim: bn
and an =
satisfy
nP
n2 Inn
(1) 0 < an <bn for all large n > 2 or
(2) 0 < bn < an for all largen > 2
(please enter (1) or (2)).
IM:
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