9n Let an Зп + 1 (a) Determine whether {a,} is convergent. convergent O divergent (b) Determine whether a, is convergent. n = 1 convergent O divergent

Q: {B"}-o; ß E (-1,0) A-Converges B-Diverges C-Absolutely converges D-Conditionally converges

A: According to our answering guidelines we can answer one question at a time, therefore I have…

Q: If dn conditionally converges then Jan| converges. 2=1 2=1 True False Rationale: Reset Selection

A: We have to find the option

Q: 28. (Continuation of Exercise 27.) If E=1an converges, and if 1 > a, > 0 for all n, show that E=1 In…

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Q: 3. Use the Test for Divergence to explain why if En-0 an converges, then En=0 am must diverge.

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Q: 1 converges conditionally because lim 第-1 = 0. 2n n=1 True False Reset Selection

A: this is false becuse

Q: If gan converges and Σbn diverges, can anything be said about their term-by-term sum Σ(an + bn)?…

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Q: +o0 Σ)

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Q: 4n + 3 Use the limit comparison test to determine whether > an = Σ 20n® + 2 converges or diverges.…

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Q: 3 and Xn %3D 4-Xn-1 converges. %3D Prove that the sequence defined by x|

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Q: a) {(3N +17))(2N)} 10. Prove that the sequence {(-1)"} does not converge.

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Q: converges and find th Yn -2- Use the Monotone Convergence Theorem to show that the sequence defined…

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Q: How to determine nln(n)/(n+1)^3 is convergent or divergent?

A: To determine the sum of the series nln(n)/(n+1)^3 is convergent or divergent. Now, Apply the…

Q: /2n?

A: The given series is: ∑n=1∞(-1)n(-1)n2n2+5=∑n=1∞(-1)2nn2+5n2=∑n=1∞1n2+5n2

Q: 1+2n Determine whether the series 25n 3 converges or diverges. Show all your work. n=4 Maximum…

A: Series is convergent..

Q: 7N 8N 3) Show that converges/diverges.

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Q: (-1)* Lk=3 In k absolutely convergent, conditionally convergent, or divergent? 100

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Q: 6. Suppose a, converges. Assume the terms a, are non-zero. Prove ÷ diverges if it is true. n=1 n=1…

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Q: 1 Is (-1)"- conditionally convergent, absolutely convergent, or n In n divergent?

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Q: (-1)" converges conditionally. Inn Show that n=2

A: For the solution follow the next step.

Q: (3n)" (2n + 50)" n=1

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Q: eries is conditionally convergent th eries is convergent then it is condi - IV I, IV II

A: A series is sum of terms of an infinite sequence of numbers.

Q: 21.) Converge or diverge? Explain. En=1 3n - п!

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Q: ii. Investigate convergence or divergence of 2n + 100 3n +1). n=2

A: Given series is  ∑n=2∞-1n2n+1003n+1n

Q: 1. Determine whether n² – sin(n) is absolutely convergent, conditionally convergent, or diver n6 +…

A: Solve the following

Q: +o0 ΣΗ 1 -3 -1-n n=1

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Q: The series 2=1 1 k is divergent no conclusion absolutely convergent conditionally convergent

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Q: 1 1 +,++ 1 1 1 1 x = _ а а b and let and Dn On n-1 be, respectively, the last and Qn-1 last but one…

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Q: 3. Determine whether E (-1)" converges absolutely, conditionally or diverges. Explain.

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Q: 5n – 1 8) Σ 7n n=1

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

A: The given series,    ∑k=1∞-1kk12

Q: (b) Give an example of divergent sequences {a,} and {b,} such that {a, + bn} converges.

A: To give an example The sequences {an} and {bn} are divergent sequence such that{an+bn} converges.

Q: 1) (am) is not convergent but (a,(a, - 2)) is convergent.

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Q: 34. Assume that an+1/an converges to p = 4. -1 Does > an converge (assume that n=1 An # 0 for all…

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Q: , 2η En=1 3 er

A: Given series is ∑n=1∞ n2nen3. Here, an=n2nen3.

Q: 6 Let an 3n + 1 (a) Determine whether {a,} is convergent. convergent O divergent (b) Determine…

A: We can find the answer as below.

Q: an2

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Q: 4n Determine whether {} 5n+1 is convergent or divergent.

A: A sequence {an} is convergent if limn→∞an=l, where l is a finite real number.A sequence {an} is…

Q: The series 1 k ln k k=2 converges. Choose an option: ()Real ()False

A: Integral Test : Suppose that f(x) is a continuous , positive and decreasing function on the interval…

Q: 2n Let an %3D 3n + 1 (a) Determine whether (a,} is convergent. convergent divergent (b) Determine…

A: Given: an=2n3n+1

Q: Let an 6n 2n + 1 (a) Determine whether {a} is convergent. O convergent divergent = (b) Determine…

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Q: 4n Determine whether Σ: 5n+1 is convergent or divergent.

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Q: n+ 7) ) Σ n2 n=1

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Q: Series that diverge absolutely may conditionally converge O True O False

A: Ans is   True.

Q: Consider an = V4n² + 3n – 2n for n > 1. (a) Determine if {an}-1 is convergent or divergent n=1 (b)…

A: a) Given an = 4n2+ 3n   -2n Rationalize (4n2+ 3n  - 2n) (  4n2+ 3n  +  2n) (  4n2+ 3n  +  2n) = (…

Q: 2) In a, = (1+-)" {a,}is convergent. show that the %3D n

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Q: Inx? x² –1, 2 x=2 A-Converges B-Diverges C- Absolutely converges D-Conditionally converges 8.

A: In both cases we use comparison test.

Q: N + 1 2N 2) Show that converges/diverges. N-1

A: The given series is: ∑N=1∞N+12N+1 Let. aN=N+12N+1,N≥1

Q: 4. Determine whether the scrics is absolutely convergent, conditionally convergent, or divergent. k…

A: Here we have, ∑k=1∞-1kkk3+2=∑k=1∞-1kak

Q: Determine whether (an + bn) is convergent or divergent. n=1

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Q: 17n + 3 Determine whether the sequence an converges or diverges. If it converges, find the limit.…

A: