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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
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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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.)
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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