6n Let an 4n + 1 (a) Determine whether {a,} is convergent. O convergent O divergent 00 (b) Determine whether a, is convergent. n = 1 convergent O divergent

Q: 4n Let an = 3n + 1 (a) Determine whether {a,} is convergent. O convergent O divergent (b) Determine…

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Q: nx (a): Show that the sequences is not uniformly convergent [0, 00]. on '1-n²x2

A: Given the sequence of function fnx=nx1-n2x2, x∈[0,∞) Now , for x=0, the sequence is 0,0,0,.... this…

Q: Σ- 2n-7, 5n +2 Select one: O a. converges to 0.4 b. converges conditionally C. diverges d. converges…

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Q: 72 2n + 1 Use the root test to determine whether converges. 5n-3 n=1

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Q: 3n! 3n! Find lim State whether 2n=1 converges or diverges. n→∞ 4n!-1) 4n!-1

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Q: n - 3 - 3 converges conditionally because lim = 0. 3n + 1 3n +1 n=1 True False

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Q: Let a, = 2n+1– 2". Then, lim an %3D n-00 None of the other options the above co and the sequence…

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Q: 00 (-1)"+1 Is En=1 convergent absolutely, non-absolutely, or diverges. n+8

A: Given series is ∑n=1∞-1n+1n+8 Absolute convergent test: If ∑an converges, then ∑an converges. Let…

Q: an = lim bn Then either ,a,and b, both converge or both diverge. 2n? +n+2 ii. Use the result in (i)…

A: We have to solve given problem:

Q: 10. If * a, > 0 and an converges, then (-1)"a, diverges True False

A: Can we test the given statement as follows

Q: 6n + 2 6n+2 Let > and an 5" 5" n=1 an+1 a) Find lim n-0 an 6n+2 b) Determine whether 2 is convergent…

A: Convergence of series.

Q: 2n Let an = 3n +5 Determine whether {an} is convergent. Determine whether an is convergent.

A: To determine whether the given sequence and series is convergent or not.

Q: 3)the sequence a) Convergent converge 1. z, nln(l+-)+; = -t is n 2n-1 b) divergent c) absolutely…

A: The given sequence is zn=nln1+1n+n22n-1i.

Q: tion 35 Suppose lim an = 00 and an1> a, > 0 for all n> 1. Which of the following statements must be…

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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: Let a, = vn +1– yn. Then, lim a, = None of the other options -00 and the sequence (a,,} is divergent…

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Q: A True B False If the sequence {a}, is convergent, then the sequence {x} defined by…

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Q: Let an = 2"+1– 2". Then, lim an = %3D n-00 None of the other options O the above co and the sequence…

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Q: 6. The sequence (xn) = (3,3,3,3, ...) is .. a) not Cauchy b) unbounded c) divergent d) convergent

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Q: 17. Divergent or convergent? If convergent, show the lim n3 + 2 an 2n3 + 1

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Q: {*} An If sequences {an} and {bn }both diverges to infinity, then the sequence is bn convergent.

A: Given query is to find the statement is true or false.

Q: 4n2 Determine if the sequence {an}I with an= converges. If it converges write its limite if it…

A: Given Data The sequence formula an is:     The expression for the limit of sequence an is,

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: 3 + 2.4 + 1.92 + 1.536 + ... O convergent O divergent If it is convergent, find its sum. (If the…

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Q: 6n Let an %3D 7n + 1 (a) Determine whether {a,} is convergent. O convergent O divergent is…

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Q: 8. 2. Let an be convergent with an > 0 for all n. Now consider (an). n=1 n=1 a) Explain in words why…

A: a) Given that series an is convergent with an > 0.

Q: 8. True or False: If lim an = 0, then an converges. %3D n=0 (a) True (b) False

A: Solved below

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

A: Given: an=2n3n+1

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

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Q: 6n Let an 5n + 1 (a) Determine whether (a,} is convergent. convergent O divergent (b) Determine…

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Q: Let an 4n 7n + 1 (a) Determine whether {a} is convergent. convergent divergent = 8 (b) Determine…

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Q: IV. Determine if the given is convergent or divergent. n Σ #2. (n² + 1)2 n=1

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Q: 3n Let an 7n + 1 (a) Determine whether {a,} is convergent. convergent divergent (b) Determine…

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Q: 5 2n Determine if the sequence {4} converges or diverges. If it converges, find its limit: 3n 7…

A: To determine the limit of the sequence.

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

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Q: 2n Let an = 3n +1° (a) Determine whether {a„} is convergent. (b) Determine whether a, is convergent.

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Q: 5n Let an 6n + 1 (a) Determine whether {a,} is convergent. convergent divergent 00 (b) Determine…

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Q: 5n Let an %3D 4n + 1 (a) Determine whether {a,} is convergent. convergent O divergent 00 (b)…

A: Given -  an = 5n4n + 1We have to determine-(1) Whether an is convergent or divergent.(2) Whether ∑n…

Q: 7) : Determine if absolutely convergent, conditionally Question # convergent, or divergent.…

A: We use definition of a absolutly convergent series

Q: 39 and 47 please ??

A: You have posted multiple questions. As per the instruction, we will be answering only the first one…

Q: 6. If > an converges but >lan] diverges then we can be sure that n=1 n=1 (a) an converges…

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Q: 2n Let an= 7n + 1 (a) Determine whether (an} is convergent. convergent divergent (b) Determine…

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Q: 1 25 +1 125 - O convergent divergent If it is convergent, find its sum. (If an answer does not…

A: Explanation of the solution is given below...

Q: 1. Determine whether 2n-1 2 nev converges. Prove your answer.

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Q: 7" (f) í(-8)*- n=1 Converges or Diverges: Sum(If Converges):

A: As this is a multiple question, according to the Bartleby answering rule, only first question is to…

Q: (-3)" converges or diverges. Vn Determine whether n=1

A: ∑n=1∞-3nn Here, an=-3nn

Q: (-1)"(7n + 1) Does En=1 converge or diverge? (3n + 1)

A: Alternating series test: If infinite series is If any of these two conditions does not hold, then…

Q: (d) Let an = 6n²+ n-1 ntn and bn √n n+1' (i) Determine whether {an} is convergent or divergent.…

A: Given;  an=(6n2+n-1) /(n2+n)  bn=sqrt(n)/(n+1)

Q: 7n Let an %3D 8n + 1 (a) Determine whether (a,) is convergent. convergent O divergent DO (b)…

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