n· 3n 5n n=

Q: +00 1 xln"(ex)

A:

Q: 1 En=1 4n² 8n +3

A: ∑n=1+∞ 14n2-8n+3using limit comparison testlimn→∞ 14n2-8n+31n2limn→∞ n24n2-8n+3factorisinglimn→∞…

Q: Σ 2n n? + 2n h= 1

A:

Q: - 1)n (n + 1)!) 3n!

A:

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

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

A: Please see the below picture for detailed solution.

Q: IV. Determine if the given is convergent or divergent. n Σ #2. L in? + 1)² n=1 %23

A: To find Whether the series converges or diverges.

Q: 52n 5n +1 n=1

A: Given that:- ∑n=1∞52n5n+1To find:- chek whather the series is convergent or divergentSolution:-limit…

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

A:

Q: 10n2 + 18 Σ 7η2+ 16η+ 21 n=1

A:

Q: In n 2 n n=1

A: Given the series

Q: (-1)* Lk=3 In k absolutely convergent, conditionally convergent, or divergent? 100

A:

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

A:

Q: · E In (e + +) n = 1

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Q: n 2n – 1 n=1 Does this diverge or converge? Explain your answer.

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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 {?n } is convergent. and determine whether ∑ ?n as n approaches +∞ from ?=1 is…

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Q: 3 - If E is convergent, find its sum. z=1 en n(n+3)

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

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Q: 5n – 1 8) Σ 7n n=1

A:

Q: Apply the Ratio Test to determine convergence or divergence, or state that the Ratio Test is…

A: Given that: ∑n=1∞enn!

Q: e-n n(n + 1) E(-1)"+1. n=l

A:

Q: , 2η En=1 3 er

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

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: (-1)" In(n) Vn n=2

A:

Q: 1 'n² – n-6 n=4

A:

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

A:

Q: 211 8. Determine whether {(1+2)"} 5c1+系) Q8 Converges or diverges.

A: Series and sequences

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

A:

Q: Vn7 +n Vnº + n5 n=1

A: Let's find.

Q: n+ 7) ) Σ n2 n=1

A:

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

A:

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

A: Given series is ∑n=2∞n2+2nn

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

A:

Q: Determine if the following converge or diverge. Explain your answer: 00 Σ) 4n+1. In=1

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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: 5. E-1 ne-" n=D1

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

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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

Q: Σ 1. 4n n=1

A:

Q: +00 Inn E(-1)": n2 n=2

A: Solution

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

A: ∑n=1∞-3nn Here, an=-3nn

Q: n! Determine whether E- converges or diverges. Zn=0

A:

Q: n? Use an appropriate method to determine if converges or diverges. n³ +1

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

A: