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

Q: Σ 2n n? + 2n h= 1

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

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Q: 2* converge? If so, what does it converge to? If not, justify. 7k 1 2 2. Does

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Q: 1 ·d. -? (r+1)2

A: We have to calculate the given definite integral according to the given information

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: Spow it the arics is absolutely convergent, conditionally convergent, or diverg ent. (using…

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Q: /2n?

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

Q: 10n2 + 18 Σ 7η2+ 16η+ 21 n=1

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Q: In n 2 n n=1

A: Given the series

Q: Determine whether sum ((5n12 +1)1/3 )/((3n12 -1)1/2) converges or diverges.

A: Given series is

Q: Š V2n-5 n=1 n2- 3n +4

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Q: Determine whether the following is convergent or divergent and justify

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

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

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Q: Σ (-1)*2* Use the Ratio Test to determine whether converges absolutely diverges. or k! k=1

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Q: +o0 ΣΗ 1 -3 -1-n n=1

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Q: Determine whether> ()" diverges. If it converges, find the converges or sum.

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Q: 8. 4+n2

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Q: (n2 +1)2 n=1 2.

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Q: 5n – 1 8) Σ 7n n=1

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Q: Q.2)(A) Determine (215) ² Σ (5)(2+1) of each point convergens or diverges: 13.0

A: Given

Q: Determine whether k- 3k+2 22k+1 converges or diverges. k=2

A: Given that: ∑k=2∞k.3k+222k+1   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: n2 + 5 Use the ratio test to determine whether converges or diverges. 5" n=11

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

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

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

Q: 1 1. Determine whether I = dr converges or diverges. If it converges, find its value. (6 13/17

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Q: 9. Determine whether the following is convergent or divergent +(-1)"+1 n! 2n 2e

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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: K3-2

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

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Q: 1 -2 (x+1)²

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Q: 3- a- By definition show that (x,) = (+3) converges to 3. b- Does (+3) bounded, Cauchy? Show by part…

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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: n2 3" 1) > 6n+1 n=1

A: Given query is to find the series converging or diverging.

Q: Determine whether 5- 2AK converges or diverges. If it converges, find the sum. k=2

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Q: Is the statement always, sometimes or never true? Briefly explain in words. (-1)"a, converges, then…

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

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Q: Vn7 +n Vnº + n5 n=1

A: Let's find.

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

A: Given series is ∑n=2∞n2+2nn

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: 3k2 Use the Root Test to determine whether converges absolutely or diverges. 2k2 + 4 k=1 IM:

A: We will solve the following

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

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Q: 3k k 18.) Converge or diverge? Explain. Ek=1 5k-1,

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Q: n3" E(-1)"; 22n+1 n=1

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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: Determine whether ∞∑n=1n√3 converges or diverges.

A: The given series is Now, the nth term of series is