25. Choose the series that is convergent: ΑΣ A) 1+ n n+1 B ) Σ- 2 n n 4n n1 ο Σ7m 3 n n 2 D Σν+1 +4n 2 3P E ) Σ 5"+1

Q: Which of the following series is conditionally convergent? [(-1)". In n 1.0015 O O O O O A B U E A)…

A: Please see the below picture for detailed solution.

Q: 10 Prove whether the series converges or diverges. cos(nn) a) E 2n-1 b) Σ c) E '(n!)² (2n)!

A: By ratio test and Lebinitz test we can give the answer for both questions.

Q: 3. Determine which of the following series converge: (a) ( d) Σ 50 + 2n n= n=1 n O n (e) n=1 (2n2 –…

A: Please note that according to guidelines only first 3subparts is solved.

Q: 9. Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

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Q: If n'h partial sum of the series i=| ak k31 is s, = ( 3n-1)2n %3D 3n then Li=1 ak =

A: The nth partial sum is Sn=3n-13n2n The  we have to find ∑k=1∞ak

Q: 3 for all n2 1. Then 2" Σ E x, be a series such that 0Sxns Let

A:

Q: 7. Determine whether the series Σn=1 n 5n 6n+2 is convergent or divergent.

A: Necessary condition for convergence  :                         Necessary condition for…

Q: O Find the N-th partial sum SN = ), → n2-1 of the infinite series n² – 1' n=2 n=2 M8

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Q: Could I get help with parts A-D?

A: According to the given information it is required to check whether the given series is absolutely…

Q: If the nth partial sum of the series 2n²+3 E an is Sn = in=1 3n²+1 then Ln=1 an

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Q: A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent.…

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Q: For which series monotone and bounded sequences theorem can be applied for the convergency? 2" I)…

A: Given that an=2n(n+2)!, an=n!nn, an=1.3.5...(2n-1)(2n+1)2.4.6...(2n)(2n+2) The monotone and bounded…

Q: Obtain the sum of the seri Ean $a = -² 2 n=2 nn

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Q: (-1)" 2) The series n=1 is п a) Convergent, but not absolute b) Converges absolutely c) Diverges

A: Answer and explanation is given below...

Q: а) nyn n=1 Σ >(-1)n+1 п c) 2" n=1 00 e) 2(-1)n+1, en n=1

A:

Q: 23. Choose the series that converges: 2" b) Σ (n+1)! Θ ΣΙ2--] 3 Ο Σ 2 n-1 n=1 n-0 1 d) ο Σ n e) n=1…

A: a) Here, we find first few partial sum ,since lim sn as n approaches infinity does not exist.…

Q: Determine whether the series is convergent or divergent by using an appropriate test: cos(2n²+3)+2…

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Q: 2. Find the sum of the series if 0 < x < c < 1: a) En³x" n=0 x" b) E n=1 (n + 1)

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Which one of the following series is divergent? 1 1 (A) E (B) E 2n + n + 1 n2 + Vn n=1 n=2 1 (C) E…

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Q: 3. Determine which of the fol 2" (a) n=1 n! (d 1 (b) (e n=1 2n 3n n+1 (c) (E 3n n=1

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: Which of the given series are convergent. 00 (-4)3п а) 2n+1 n=1 2"n! b) 2 3^(2n)! (n + 2) n=1 2n3 -…

A: To find- if the series is convergent.

Q: If the nth partial sum of a series an is n = 1 Sn a 1 = 00 Find an and Ear an n = 1 an Σ an n = 1 =…

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Q: Q2) The summation of ex series is x" a) En=0 n! b) Σ-01 5+n! xn+1 c) En=0 (п-1)! d)

A: Given:   Let fx=ex To find the Maclaurin series coefficients, we must evaluate          dndxnfxx=0…

Q: 1) (-1)*- n² 2" n=1 a) Show that the series is convergent. Show All Your Work!

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Q: Q1: A- Find the limits of the following series (-1)" ܐ R=0 22 Στη Σ iv- 6 (2n-1X2n+)

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Q: a) Is the series sin(n) Σ is – 7n + 1 n³ + 3n² n=1 absolutely convergent or divergent? justify your…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: what the absolute convergent, conditionally are divergent ,and divergent series among the following…

A: Since you have asked multiple question , we will solve the first question for you. If you want any…