5 sin n 11. Use the direct comparison test to show that converges. n! n-1 5 sin n 5. 5 sin n converges, so n-1 converges as well. n! n! n! * In n 12

Q: To test this series for convergence n n=1 Vn6 + 6 1 where p= You could use the Limit Comparison…

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Q: | converges to p What can you say about the convergence of the giver (Enter 'inf for o.)

A: We have to choose the correct answer from the given options according to the given information

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Q: Find the interval of convergence for the series below: 11"(포")(n + 1) (n + 4) n=1 The series is…

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Q: Determine the convergence or divergence of the series. 00 cos(nTt) n = 1 O converges O diverges

A: The correct option is “diverges”. Expand the given series.

Q: Find the series radius and interval of convergence for what values of x does the series converge x"…

A: We need to find radius and interval of convergence.

Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. Σ sin (n) n…

A: The given series is convergent.

Q: The following telescoping series tan 1( n +2 tan n + 1 n=1 converges to – tan(0.5) converges to…

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Q: To test this series for convergence n nº + 4 n=1 where p= пр n=1 You could use the Limit Comparison…

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Q: Consider the series ak where (k!)² [(2k)!]² ak In this problem you must attempt to use the Ratio…

A: Given that ak=k!2(2k)!2or, L=limk→∞(k+1)!2(2(k+1))!2k!2(2k)!2or,…

Q: To test this series for convergence n 3 n³ + 7 n=1 1 where p= You could use the Limit Comparison…

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 1 3n7 + 8 n…

A: Given series is ∑n=1∞13n7+8. We have to check whether the series ∑n=1∞13n7+8 is converges or…

Q: Which of the followings are true? I. En-1 |sin-|converges by comparing with 1. II. En-1 converges by…

A: Have to check whether the given series are convergent or not. I sinx≤x By using this we can say that…

Q: The radius of convergence for the series En=o(-1)" (x+9)" is n²+1 O NONE

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Q: f the limit of the nth term of a series converges to 0, then the series onverges.

A: This is the false statement. So i am providing an example in my handwritten note, so that it'll be…

Q: To test this series for convergence n4 + 3 n=1 1 where p= You could use the Limit Comparison Test,…

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Q: To test this series for convergence n + 6 n=1 1 where p= np You could use the Limit Comparison Test,…

A: Use limit comparison test for check the convergence of series.

Q: To test this series for convergence n /nª + 7 n=1 You could use the Limit Comparison Test, comparing…

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Q: Q10) The series 4n Σ n =1 n²+2 a) converges to b) converges by comparison test th term test c)…

A: To find- The series ∑n=1∞4nn2 + 2  Converges to 0 Converges by Comparison test Converges by nth…

Q: To test this series for convergence n° + 3 п4 — 4 n=1 You could use the Limit Comparison Test,…

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Q: To test this series for convergence 4" – 7 4" n=1 You could use the Limit Comparison Test, comparing…

A: step:-1 nth Term Test / Divergence Test:- Let ∑n=1∞un   be a series  if limn→∞un=a 1. if a ≠0 then…

Q: Find all values of x where the given series converges. 9" x" (n + 1) n + 9 n=1 Answer: Note: Give…

A: Given ∑n=1∞9nxnn+1n+9

Q: Use the ratio test to determine whether a_n converges,where a_n is given in the following problems.…

A: The solution are next step

Q: > ke 10 k=1

A: The given series,      ∑k=1∞k e-110k2

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 00 sin“(n)…

A: We have to find the convergence of series

Q: Vn +2 Use the limit comparison test to determine whether the series ) converges nª + 4 n=1 or…

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Q: The series O True O False Σ (-1)^+1 n=2 n3+1 is absolutely convergent.

A: The given series is summation of (-1)n+1/(n3+1), n from 2 to infinity.

Q: To test this series for convergence 67 4 n=1 You could use the Limit Comparison Test, comparing it…

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Q: Applying the ratio test to the series ∞ 5k-1 k=1 (k+ 1)².4k ³ you would compute ak+1 lim = ak Hence…

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Q: 27 n + 191 The sequence tan 9 n + 169 n=1 O converges to 3 O converges to 6. O diverges converges to…

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Q: (A) True B) False The sequence {x}to, where xn = Sn² 20" is convergent. n! :

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Q: The series True O False Σ n=1 (-1)"-3 √n is absolutely convergent.

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Q: 2n +1 a) n=1 3n-5 WE

A: Solution:Given  ∑n=1∞ 2n+13n-5To find the nth term test say about the convergence of the series.

Q: For which an does the sequence {an}-1 converge? Select all that apply. OA. sin(3n) an n2 OB. Зп — 1…

A: We will answer the first three parts for you. Kindly repost the question specifying the desired…

Q: To test this series for convergence n° +. 00 n6 – 3 n=1 You could use the Limit Comparison Test,…

A: Given query is to find the limit of the expression.

Q: Yo2n +5 The series Converges to 4 Converges to -1/2 Diverges Converges to 1/4 Converges to 1/2

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Q: We are asked to find the values of p such that the following series converges. 4 2 n(In(n))P n = 2…

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. Š sin (n)…

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Q: 6. SELECT ALL APPLICABLE C A) converges by root test 1 10n+1+(-1y" B) converges by ratio test B D. E…

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Q: 2" Use the ratio test to determine whether >. (2n)! converges or diverges. n=17 he ratio of…

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Q: * 3" +n 2) Use the Comparison Test to determine whether the series or divergent. Show All Your Work.…

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Q: 3 Sn n+1 n+2 Show sequence { Sn} give in converaent. that the general ter Ms is

A: 3 Given that Sn=1n+1+1n+2+........+12n. We have to show that the sequence Sn is convergent. Since,…

Q: To test this series for convergence n3 + 8n? + 1 L 7n7 + nổ + 2 n=1 You could use the Limit…

A: Using limit comparison test

Q: The series n=4 is convergent. The term a29 of the sequence {a,) given by 2 3 4 5 5'7'9' 11 is 31 63…

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Q: To test this series for convergence n Vnô + 7 n=1 00 1 where p= You could use the Limit Comparison…

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Q: Let > an be a convergent series. n=0 Does the series ) cos(an) converge? Explain! n=0 nx" Find the…

A: In this question, we need to check the convergence of the series and in the second part we need to…

Q: -st to show that the first series diverges by ca n2 +n n3 – 2 n=2 n=2

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Q: The series 2 1 is convergent. n =1 n(2) Select one: O True O False

A: