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

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A: ∑k=1∞3k+4k5k

Q: n=1 (ii) Give an example such that a, converges conditionally and diverges. IM:

A: Please see the below picture for detailed solution.

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Q: (-1)" Determine whether E1 converges absolutely, converges conditionally or stify your answer by…

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

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

A: Option 3 is correct.

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A: Explanation of the answer is as follows

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A: To determine whether series converges or divergent.  Here by using ratio test we will determine…

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Q: Σ Show that n2 + 1 converges/diverges n

A: The given series is: ∑n=1∞nn2+1 Let  an=nn2+1,n≥1    =nn21+1n2   =1n1+1n2 And, bn=1n

Q: 1 3. En=1 (2n+1)3

A:

Q: 5n – 1 8) Σ 7n n=1

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Q: Determine whether E=1(-1)"+1. 2n converges or diverges. If it converges, find the sum. 3n

A:

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

A: The given series,    ∑k=1∞-1kk12

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

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

Q: 00 n=1 n² -4.

A:

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

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Q: +00 El-1)» (" – n)" 2η n=1

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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: Determine whether r{(1+E)*"}.. Converges or diverges.

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Q: 1 7. Determine by the ratio test if n- converges or diverges. п! -

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Q: 1 -2 (x+1)²

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Q: ,(-1)" converges conditionally, but not absolutely. Show all work. 3n Prove E

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

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Q: (1) Show that n2 +1 n=1 converges conditionally. Show that all conditions of the test used are…

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Q: Determine whether the scries is absolutely convergent, conditionally convergent, or divergent. (a) E…

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Q: n· 3n 5n n=

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

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

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A: According to the given information, Suppose,

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A: If absolut series is divergent than alternate series is convergent.

Q: Find the values of p such that E(-1)"- converges.

A: The given series :

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A:

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: 3k 5- 2k+1 k=1 2 1. Does converge? If so, what does it converge to? If not, justify.

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Q: (-1y" In n 1) Determine if £∞ n=1 Absolutely converges, converges conditionally, or diverges.

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Q: 6n2 n

A: The given sequence be 6n2en To find it is convergent or divergent