Prove that the sequence given by 2.4. 6.(2n) Un = 3.5.7.…(2n + 1) converges and find its limit.

Q: Determine whether the following sequence is convergent or divergent. Justify your answer {Vn- Vn+1}

A: We need to determine that sequence n-n+1 is convergent or not.

Q: Determine whether the given sequence converges or diverges. If it converges, calculate its limit. an…

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Q: Prove that the sequence (xn) = (-1)"+1 [3 .does not converge to any real number

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Q: The value ofk that makes the following sequence is converge to * : (7/6) as n approach to infinity…

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Q: Show that the sequence defined by 1 a₁ = 1 an is increasing and an < 3 for all n. Deduce that {an}…

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Q: Consider the sequences (an) and (bn) given by an= (−1)nn2, and bn= 2n. Decide if the sequence…

A: Convergency for an:we can find limitwe know that (-1)^n is oscillating This value can be either -1…

Q: Determine whether the following sequence converges or diverges. If it converges, find its limit. 40n…

A: One simplest method to calculate whether sequence converge or diverge is calculate sequence at n…

Q: Consider the following.sequence: (-1)*+1 n2 {a,} n=1 (a) Write out the first five terms of the…

A: Given the sequence an = (-1)n+1n2n=1+∞

Q: Determine whether the sequence is convergent or diver- gent. If it is convergent, find its limit. 2…

A: Given :  The sequence an = 2 + n31 + 2n3   To determine the sequence is convergent or divergent.

Q: 3 Show that the (sn} sequence given in general terms converges. Sn + n+2 n+1 2n +

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Q: 2. Define a sequence (a) by a=1, an+1 dn Vn E N. (n + 1)2 Does the sequence converge? Find the limit…

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Q: Compute the first six terms of the sequence {an} = {n√n}. If the sequence converges, find its limit.

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Q: Determine whether the following sequence converges or diverges. If it converges, find 3" where n >…

A: The given sequence is: an=3nn! ;           where  n≥1

Q: The sequence an = n – Vn +1yn+3 converges to the limit

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Q: Find the limit of the following sequence or determine that the sequence diverges. {(n sin3…

A: Given:  Calculations: Calculate the following limit

Q: Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each…

A: Given: Calculations: Compute the following limit

Q: Suppose that is a convergent sequence and {an} 3n a, = 12· lim 2n+1) Find lim an. O48 OB. 18 OC12…

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Q: 10. Determine if the following sequence an = In(n)/In(2n) converges or diverges as limit no. Find…

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Q: 3. Determine if the sequence xn = 47² is convergent or not and find its limit if it exists n²+1

A: We want to find the given sequence is convergent or divergent.

Q: The sequence {5}"-1 is: is: 00 O Converges to 10 O Converges to Converges to 5 Diverges. H/5

A: The given sequence is: 5n=1∞

Q: 1. Determine which of the following sequences converges, and which diverges? If a sequence…

A: A real monotonically decreasing sequence is said to be convergent if it is bounded below by a real…

Q: Is {3n/(3n-1)} n=1 to infinity, a convergent sequence in R with the usual metric dR(x,y) = abs(x-y)?

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Q: State if the sequence {xn}1 define below is convergent or divergent: fix -1< a < 1, and let xn =…

A: The convergence of the series can be checked by applying the limits to ∞. The convergence of the…

Q: 3. Prove that the sequence sin(n) (0, 1). converges to n n+1

A: We calculate both limit separately as n tends to infinity.

Q: 72 a, = 5, an +1-1+ an

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Q: 1. Prove that the sequence {4+} converges to 4.

A: To know weather two function converge or not take difference of them and put limit to infinite. If…

Q: Consider the sequence defined by a, = In(2n³ + 2) – In(5n³+2n² + 4). Find the limit of an as n → ∞.…

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Q: Write out first five terms of the sequences, determine whether, the sequence converges, and if so,…

A: We have to find the limit of the sequence and find first five terms

Q: 7. Determine whether the sequence, n 1+4n² 1+n² > converges or diverges. If it converges, find its…

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Q: 1. Prove that the sequence converges to . 2n+1

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Q: Prove that the sequence defined by a1 = −3 and an+1 = 14 (2an-1) converges. Then prove that it…

A: Given a sequence with recursive formula,  a1=-3, an+1=142an-1 To prove that the sequence converges.…

Q: Suppose (xn) is Cauchy and (yn) is bounded and monotone. Can we say anything about whether the…

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Q: 2. Use the definition to prove that if (xn) is a sequence of real numbers which converges to -3,…

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Q: 10. Determine if the following sequence a, = In(n)/In(2n) converges or diverges as limit no. Find…

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Q: Determine if the following sequence converges or diverges and find the limit if possible. Sin(n+ 1)…

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Q: 2. Use the definition to prove that if (xn) is a sequence of real numbers which converges to -3,…

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Q: Find the limit of the following sequence or determine that the sequence diverges. {(sin n)/(2n)}

A: The sequence an is called convergent if limn→∞an is a constant real number.

Q: prove that the sequence (1/5^n) is convergent and approaches zero?

A: Series and sequences

Q: 5. Show that the infinite sequence a, = Vn2 + 1 – yn² – 1 (n 1) converges by showing that it is…

A: Given sequence is  an= √(n^2+1) - √(n^2-1)

Q: Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each…

A: an=ln2n+1n Now, limn→∞an=limn→∞ln2n+1n=limn→∞12n+1·21       By using L'Hospital's…

Q: Determine whether the following sequence is convergent or divergent. Justify your answer. {Vñ -…

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Q: Determine if the sequence converges or diverges. If it converges, state the limit. an nsin = in 1.²1…

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Q: an Show that if lim bn =0 and =1 n- 00 converges then En=1ªn converges too. n=D1

A: We have to solve given problem:

Q: an = 0 and bn Σ-1 bp Show that if lim n converges then En-1an converges too.

A: Given that:            limn→∞anbn=0 and ∑n=1∞bn converges. Prove ∑n=1∞an converges.

Q: The sequence a = is a divergent sequence o converges to 8 none O converges to 0

A: Given: an=8nn For sequence, an, if limn→∞an+1an&gt;1, then sequence is divergent.

Q: 2. Determine whether the following sequence converges or diverges. If it converges, find its limit.…

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Q: The sequence an = n- -In+1vn +3 converges to the limit %3D A) -3 B) -1 C) 1 D) +2 E) -2

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Q: Show that the infinite sequence 5. an = √ (n2 + 1) − √ (n2 − 1) (n ≥ 1) converges by showing that it…

A: Given sequence is  an = √ (n2 + 1) − √ (n2 − 1) (n ≥ 1)

Q: an = In(3n2 + 1) – In (n² + 1)

A: For the solution follow the next step.