diverges if it is true. an n=1 Suppose > an converges. Assume the terms an are non-zero. Prove > n=1 If it is not true, provide an example to illustrate this.

Q: If 2a, converges, then 1. diverges Select one: True False

A: Use the defination of convergence of a series.

Q: If lim an 1 then n00 Σ an n=1 converges O diverges O may or may not converge

A:

Q: la) 을 In ? n=2 16) n=2

A: The solution of given problem is given as follows :

Q: 8. Determine by the ratio test if 2n=1 (2n)! converges or diverges.

A:

Q: N! 9) Show that converges/diverges

A: Use D Alembert ratio test

Q: 1 n=2 n(Inn)P -4

A: We need to find the value of p for which series convergent.

Q: If > an converges then an converges.

A: Absolutely true.

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

A:

Q: The sequence (n+(-1)" n Diverges Converges to 0 Converges to 1 Converges to e Converges to 2e

A: Option 3 is correct.

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

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Q: 2n + 5 9n + 4 n=1

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Q: · E In (e + +) n = 1

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Q: evaluate. Does the series ∞[4 2^k(x-3)^k/2k converge absolutely, converge conditionally or diverge?…

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Q: Verify if the resulting series of constant terms when x = 0 is absolutely convergent, conditionally…

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Q: Determine whether En=1n?e- converges or diverges.

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

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Q: The interval of converge Use your own wo each step) that yo

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Q: Determine if the following converge or diverge.

A:

Q: Corver Is absdutely contergent, Conditionally Convergent, on divergent

A: Use Alternating series test, P- series test

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: H) IM:

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Q: 2 n 1 o Show that + converges/diverges n-

A:

Q: If an> 0 and Σ an converges, then Σ(-1)"an converges.

A: We have to check wheather it is true or not

Q: The series 1(-1)" converges to 0. True False

A: We have to find if the given series is converges.

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

A: We have to show whether the series converges or diverges.

Q: , 2η En=1 3 er

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

Q: 22n Σ n! n=1

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Q: an2

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Q: K3-2

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Q: 1 1+ 2/2' 3/38 1 1 + 1 + ... 5/5 +

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Q: F) nー1

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Q: 1 Determine if dr converges or diverges. If convergent, find its value. (In r21

A: Given: ∫0∞1x1+ln x2dx

Q: A) diverges B) converges

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: show : ΣΣ - a"d, (x - a)" | n=0 m=0 is convergent,

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Q: If an converge to zero then the series -0 an is convergente Select one: True False

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Q: The series 3 k 1 3. is 3. convergent to O None divergent convergent to 3 convergent to

A: We have to solve

Q: Determine whether the sequenceconverges or diverges. If it converges, find its limit. an = cos2n/4n

A: Consider the given sequence. an=cos2n4n A sequence is said to be absolutely convergent. If an is…

Q: Note: If it converges, consider whether it is geometric or telescoping and enter its sum. If it…

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Q: Determine if the sequence converges or diverges. If it converges, state the limit. an nsin = in 1.²1…

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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: If 2(-1)" a, is absolutely convergente the n=0 na, is divergente. Select one: O True O False

A: Topic:- sequence and series

Q: Determine if the following is convergent or divergent: a dr

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

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Q: Determine if the following is convergent or divergent: I dr

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Q: 2sys8 y > 8 Show that Y converges in probability to a constant, and provide that constant.

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Q: The sequence fn(x) = is 72 Select one: a. diverges Ob. converges uniformly but not pointwise C.…

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