Diin (n) Converges or diverges (n+4)3 21

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

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Q: Find all real numbers k so that the series (n – 3)* + (n – 3) (n³ – n³ – 1)'/3 n=4 converges.

A: Explanation of the answer is as follows

Q: Is the statement always, sometimes, or never true?

A: a) Let Sn and Tn be the nth partial sum of the series with nth term an and bn. Since the series…

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

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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: conditionally convergent, absolutely convergent or divergent  En=2 (-1)n+1ln(n)/n

A: Absolutely convergent: ∑n=1∞-1n an is a absolutely convergent if and only if positive term series…

Q: (a) Provide an example of a sequence (an)neN such that a2m → 2 but (an)nen does not converge to 2.…

A: To find find the example of the given sequence that satisfy the above condition .

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

A: Can we test the given statement as follows

Q: n n converges, because 0 < < 1 and an 2n + 1 2n + 1 ni an is decreasing. 2n + 1 True False

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Q: (-1)k-1) k4/3 Determine whether 6. converges absolutely, converges conditionally, k=1 or diverges.

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Q: 21. Show that E(-1)"+1; 2n converges n! absolutely. n=1

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Q: 1 n (In(n))³ n=2

A: To find that series converges or diverges

Q: { II. Consider the sequence í n+ 2)! J n=1 a.) Show that the given sequence is monotone. b.) Use the…

A: Here, the given sequence is: πn(n+2)!n=1∞ Let, an=πn(n+2)!

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: n - 3 п - 3 1 (-1)" converges absolutely because 0 3. Зп + 1 Зп + 1 n=1

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Q: True or False? Prove your answer! Suppose  (an)  is a sequence whose terms are all positive and…

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Q: 3. 4. En=12 () 4,

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Q: 7.) n=1

A: The given series

Q: • (-1) k2k k² k=1 Use the Ratio Test to determine whether converges absolutely or diverges.

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Q: Determine whether the series converges or diverges.

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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: (-1)" converges absolutely, conditionally, or not at all. Determine if n! n=1

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Q: 5(-7)" n2 n=1 A-Converges B-Diverges C-Absolutely converges D-Conditionally converges C 8.

A: Given series∑n=1∞(-7)nn2 Now we can test convergence of series by Ratio test as follows

Q: 87 The sequence a = is %3D a divergent sequence O converges to 0 o converges to 8 none

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Q: Van converges. Show that if a, > 0 and a, converges, then п п31 n=1

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Q: Σ n = 1 n" converges Select one: True False

A: To find whether system converge is true or false.

Q: a, > 0 and Ea, converges, then (-1)"an converges O False O True

A: This is Not True. Hence False is the correct answer. We will prove this by taking an example, Let…

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

A: use the basic property of sequence and series

Q: (2n)! Σ n2n converges n = 1 Select one: True False

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Q: (k + 1)/2 (k5 + k3 – 1)/3 1. Show that converges. k=1

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Q: olutely convergent, conditionally convergent, or ergent. |(-3)n² / (n + 1)! E (-3)" / (2n² + 4") 2…

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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: n Σ=o(-1)n+1 (는) absolutely converges, conditionally converges or diverges. 12. Determine if

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Q: 2n converges or diverges. (2n)! n=30

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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: Does it converge or diverge? Σ 2 + 2n' n=2

A: Given series is ∑n=2∞n2+2nn

Q: 8. If (an)n-1 is a monotone sequenee, then (a,)n=1s convergent. %3D1

A: Disclaimer: Since you have asked multiple questions we will solve the first question for you. If you…

Q: converges or diverges. n³ + n² – 2n n n4 -8n2 +1 n=1

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Q: What test would you use to test the convergenc 2n+1 n=1 n³-4n²+6 2. ΣΤ-1 (-1)"+1 (n²+3)² 3. Σ-1 5sec…

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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: 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: 1 N-1 Show that the series N converges/diverges

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Q: 3. Find all values of x such that the series > (x – 6)" is convergent. n=1

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

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

A: ∑n=1∞-3nn Here, an=-3nn

Q: 2. True or False? Prove your answer! Suppose (an) is a sequence whose terms are all positive and…

A: Given information :  (an) is a sequence whose terms are all positive and that for every n ∈ℕ, only…