The sequence {G1)}m1 5n+3 5n+1 n=1 Diverges converges to Je3 converges to Je² converges to 0 converges to e

Q: he series (-1)". n=D0 4n Converges to 4 Converges to -1/2

A: The series is alternating series.

Q: If 2n=1a, converges, and if a„ # 1 and a,n > 0 for all n, a. Show that E=1a, converges. b. Does…

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Q: Determine whether the given converges or diverges. n Σ 2n + 1 n=1

A: Given is a series ∑n=1∞n2n+1n To check if the given series is convergent or divergent Ratio test:…

Q: a) Determine if Eº, absolutely converges, conditionally converges, or diverges. ´n=2 n-yn

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Q: Using Sandwich Theorem, the sequence 2 = 4 – - Cos2 n +1 n³ converges to 4 converges to 2 diverges…

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Q: n=1 (ii) Give an example such that a, converges conditionally and diverges. IM:

A: Please see the below picture for detailed solution.

Q: Using Sandwich Theorem, the sequence 1 cos? n + 1 an = 4 - n converges to 4 converges to 2 diverges…

A: Given

Q: In n Q10 ) The series E n n=1 3n-4, a) converges to 0 b) diverges c) converges by the root test d)…

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Q: The series 7 2n E,(-1)" 4 n= is absolutely convergent. Select one: True O False

A: Root Test : Suppose we have series ∑ an .Define,                          L = limn→∞ an1n .Then ,(…

Q: Show that E-2 ((In n)ª/n²) converges for -o 1. n=2

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Q: a n+1) %3D 2n Ans. Converges, 6)

A: Since you have posted a multiple  question according to guildlines I will solve first (Q6) question…

Q: Using Sandwich Theorem, the sequence 2 cos? n + 1 an = 4 - diverges converges to 0 converges to 2…

A: Use range of cos x which lies in -1 and 1

Q: MEDI is a) converges to 2 b) converges to 2/2 c) converges to 23 d) diverges e) None of all

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Q: The series E n4+10 is 4n2-3n3+7 (i) Converge (ii) Diverge

A: We have to calculate the limit of the given function when n tends to infinity.

Q: Find the interval of convergence of E(-1)". n 2n 36" n=0

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Q: Determine whether the given converges or diverges. n 2n +1 n=1

A: We can solve this as follows:

Q: Q3) The sequence a, = 1 - (0.2)" a) converges to 0 b) diverges c) converges to e d) converges to 1

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Q: The sequence {Pn =}1 converges n-1 to p = 0 of order a = %3D O a. 3 O b. 1 О с. 2

A: For some number p, if the condition limn→∞an+1anp=M>0 is satisfied, then the order of convergence…

Q: 13. Determine whether ∞ Σ(-1)* k1/2 k=1 converges absolutely, converges conditionally, or diverges.

A: The given series,    ∑k=1∞-1kk12

Q: 4. Let r be a positive number. Determine the value(s) of r, if any, such that converges. As n" n=1…

A: Explanation of the answer is as follows

Q: Use the root test to find the radius of convergenc n n Σ (m+-+²1) ² = xn 9n +4 n=1

A: Introduction: The radius of convergence of a energy collection is the diameter of the most important…

Q: Q9:S a)converges to 2 b)converges to 을 c)converges to - 2 d)diverges

A: Since  you have posted a multiple  question according to guildlines I will solve first  (Q9)…

Q: The series k=1 5( − 1)k+1 - kl.1 O converges diverges.

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Q: The series 2(k+2)3-k is k=1 convergent to 6 divergent convergent to 8 O None 15 convergent to 2

A: Given - A series To find - Nature of Series , i.e. Convergence or Divergence

Q: d) If Can's Converger and {b,'s diverges, Hhen fanton} Converges.

A: we argue by contradiction: suppose that an+bn converges. Since an converges by assumption, the…

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: The sequence {(1 + 1)^² +1} 2n O O converges to e² is divergent ez converges to e 2 O converges to e

A: Sequence

Q: Using Sandwich Theorem, the sequence 2 1. an = 4 sin? 3 %3D n + 1 converges to 0 converges to 2…

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Q: Vn +1- n –1 n=1

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Q: (-1)" In(n) Vn n=2

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Q: 3n 4. Use the ratio test to determine whether Σ converges. (n + 1)! n=1

A: use the ratio test for convergence of series.

Q: The sequence {G 3n+2 n=1 O None converges to e O diverges converges to Ve? converges to e3

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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: The sequence (-1)"+1 n=1 is converge to (i) Converge (ii) Diverge

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Q: In(k) Does the series ) (- 1)* E(- 1)* k2 + 4 converge absolutely, converge conditionally or…

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Q: 5. Determine whether the series E -(-1)*52a÷1 converges absolutely, converges conditionally or 25n-2…

A: Explanation of the answer is as follows

Q: The sequence (-1)n+1 In=1 converge to is (i) Converge (ii) Diverge

A: The given sequence (-1)n+1n=1∞

Q: By limit comparison test, the series 1 3n 8n+1 n3D1 9n +2 O Diverges O Converges O None of these…

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Q: Q3) The sequence a, = 1 - (0.2)" a) converges to o b) diverges c) converges to e d) converges to 1

A: Given an=1-0.2n

Q: 7n+2 5. By using Ratio Test, determine whether > converges or diverges. (n + 1)! n=1

A: The answer is found in step-2

Q: The sequence {C+1 In=2)"} N=1 converges to e² O None diverges converges to le converges to e³

A: The given sequence 3n+23n+1nn=1∞ The sequence can be written as follows:…

Q: Use the Direct Comparison Test to determine the convergence or divergence of the s 5n Σ 4n - 1 n = 1…

A: Given query is to find series converges or diverges.

Q: O Does Eo 2k+² e-k converge or diverge? If it converges find the sum. "k=1'

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Q: (n!)³ (3n)! 321. n=1 8.

A: we have to solve using ratio test

Q: 3k 5- 2k+1 k=1 2 1. Does converge? If so, what does it converge to? If not, justify.

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Q: (-1y" In n 1) Determine if £∞ n=1 Absolutely converges, converges conditionally, or diverges.

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Q: The series (-1)"n²n! 2" n=1 O converges absolutely converges conditionally O diverges diverges…

A: Given series: ∑n=1∞-1nn2n!2nHere we have to check the correct option.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.