Which test do you use to decide the-n²convergence of an where anwhat do you conclude about the series?= neandUse the limit comparison test with b,Ann²e-n°.Then lim= ∞, and sincen→∞ b,Σb, is (D), Σ α, is (D).Use the limit comparison test with bnAne-n. Then limn→∞ bn0, and sinceΣ, is (D) Σ α, is (D).None of the given options is correct.-n²Write eas cos n2 + i sin n² andapply the alternating series test to thereal and imaginary parts separately. Sinceeach term is decreasing in magnitude andtending to zero, the series is (C) by theAST. O Use the integral test with f (x) = xe'Nf(x) dx →1-1eas N →.Then210. Further, f(x) is positive anddecreasing for x > 1, so the series is (C)by the integral test.,2„x-Use the integral test with f(x) = xe¢N. Then1/ → ∞ as.f (x) dxo as N → o.Therefore the series is (D) by the integraltest.

Answered: 2 ,-n² and convergence of an where an…

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2 ,-n² and convergence of an where an what do you conclude about the series? ne

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Which test do you use to decide the
-n²
convergence of an where an
what do you conclude about the series?
= ne
and
Use the limit comparison test with b,
An
n²e-n°.Then lim
= ∞, and since
n→∞ b,
Σb, is (D), Σ α, is (D).
Use the limit comparison test with bn
An
e-n. Then lim
n→∞ bn
0, and since
Σ, is (D) Σ α, is (D).
None of the given options is correct.
-n²
Write e
as cos n2 + i sin n² and
apply the alternating series test to the
real and imaginary parts separately. Since
each term is decreasing in magnitude and
tending to zero, the series is (C) by the
AST.

O Use the integral test with f (x) = xe'
N
f(x) dx →
1
-1
e
as N →
.Then
2
1
0. Further, f(x) is positive and
decreasing for x > 1, so the series is (C)
by the integral test.
,2
„x-
Use the integral test with f(x) = xe
¢N
. Then
1/ → ∞ as.
f (x) dx
o as N → o.
Therefore the series is (D) by the integral
test.

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