Determine whether the series is convergent or divergent. n=1 10-42-2 (-4)3n+1 The series ? Justification: (If more than one test is appropriate, pick the first applicable test in the list.) OA. This is a Geometric Series of the form > apr 1 n=1 OB. This is a Telescoping Series, lim s₁ = 12 00 OC. By the Divergence Test, lim an = T->00 OD. By the Direct Comparison Test, an ≤ bn with Σbn = Σc(), c = O E. By the Direct Comparison Test, an > bn where Σ bn = [c() where c = OF. By the Limit Comparison Test, let bn = c() where c = an lim n 100 bn f(x) dx = OI. By the Ratio Test, lim n 100 an+1 an where a = = OJ. By the Root Test, limno Van = OG. By the Alternating series test, i) {b} is ultimately decreasing because the function f satisfying f(n) = bn is decreasing on the interval ii) lim bn = n-00 = , P = OH. By the Integral Test, i) The function f satisfying f(n) = a₁ is positive, continuous, and ultimately decreasing on the interval fº and p = and its sum is and p = and (Enter "DNE" if divergent.)
Determine whether the series is convergent or divergent. n=1 10-42-2 (-4)3n+1 The series ? Justification: (If more than one test is appropriate, pick the first applicable test in the list.) OA. This is a Geometric Series of the form > apr 1 n=1 OB. This is a Telescoping Series, lim s₁ = 12 00 OC. By the Divergence Test, lim an = T->00 OD. By the Direct Comparison Test, an ≤ bn with Σbn = Σc(), c = O E. By the Direct Comparison Test, an > bn where Σ bn = [c() where c = OF. By the Limit Comparison Test, let bn = c() where c = an lim n 100 bn f(x) dx = OI. By the Ratio Test, lim n 100 an+1 an where a = = OJ. By the Root Test, limno Van = OG. By the Alternating series test, i) {b} is ultimately decreasing because the function f satisfying f(n) = bn is decreasing on the interval ii) lim bn = n-00 = , P = OH. By the Integral Test, i) The function f satisfying f(n) = a₁ is positive, continuous, and ultimately decreasing on the interval fº and p = and its sum is and p = and (Enter "DNE" if divergent.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Determine whether the series is convergent or divergent.
n=1
10-42-2
(-4)3n+1
The series ?
Justification: (If more than one test is appropriate, pick the first applicable test in the list.)
OA.
This is a Geometric Series of the form >
apr 1
n=1
OB. This is a Telescoping Series, lim s₁ =
12 00
OC. By the Divergence Test, lim an =
T->00
OD. By the Direct Comparison Test, an ≤ bn with Σbn = Σc(), c =
O E. By the Direct Comparison Test, an > bn where Σ bn = [c() where c =
OF. By the Limit Comparison Test, let bn = c() where c =
an
lim
n 100 bn
f(x) dx =
OI. By the Ratio Test, lim
n 100
an+1
an
where a =
=
OJ. By the Root Test, limno Van
=
OG. By the Alternating series test,
i) {b} is ultimately decreasing because the function f satisfying f(n) = bn is decreasing on the interval
ii) lim bn =
n-00
=
, P =
OH. By the Integral Test,
i) The function f satisfying f(n) = a₁ is positive, continuous, and ultimately decreasing on the interval
fº
and p =
and its sum is
and p =
and
(Enter "DNE" if divergent.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f411bc-d64a-4c12-9b2d-d90db0cf765d%2Faaa45ae0-03bb-4c08-9e02-4535b422d990%2Fwrgx5rf_processed.png&w=3840&q=75)
Transcribed Image Text:Determine whether the series is convergent or divergent.
n=1
10-42-2
(-4)3n+1
The series ?
Justification: (If more than one test is appropriate, pick the first applicable test in the list.)
OA.
This is a Geometric Series of the form >
apr 1
n=1
OB. This is a Telescoping Series, lim s₁ =
12 00
OC. By the Divergence Test, lim an =
T->00
OD. By the Direct Comparison Test, an ≤ bn with Σbn = Σc(), c =
O E. By the Direct Comparison Test, an > bn where Σ bn = [c() where c =
OF. By the Limit Comparison Test, let bn = c() where c =
an
lim
n 100 bn
f(x) dx =
OI. By the Ratio Test, lim
n 100
an+1
an
where a =
=
OJ. By the Root Test, limno Van
=
OG. By the Alternating series test,
i) {b} is ultimately decreasing because the function f satisfying f(n) = bn is decreasing on the interval
ii) lim bn =
n-00
=
, P =
OH. By the Integral Test,
i) The function f satisfying f(n) = a₁ is positive, continuous, and ultimately decreasing on the interval
fº
and p =
and its sum is
and p =
and
(Enter "DNE" if divergent.)
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