Use the definition of the limit of a sequence to show that: mm ( 2²2 +²13) = 1/21 n (b) lim (√n² + 1 -n) = 2n²-3 (a) lim √√n+ (c) lim (√+ (-1)") = 1 +1

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

A: Answer is infinity

Q: Find the sum of the first five terms of the sequence. (Assume that the sequence is defined for n ≥…

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Q: Find the limit of the sequences with general term as given: (e) (√4 - √1/n  - 2)n (f) (-1)n √n / n…

A: Answer

Q: Suppose (xn) converges, and let K be a positive integer. Now create a sequence (yn) by changing the…

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Q: how do i apprach this problem?

A: The objective of this question is to find the limit of the sequence (n+1) as n approaches 0 using…

Q: a1 =-1, an+1= An +6 An +2

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Q: For ln(1+1/x), determine if the sequence is bounded and whether it is eventually monotone,…

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Q: (6) Let {an} be the sequence defined by an+1 = √6an 2, a₁ = 1. Show that {an} is converger and find…

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Q: 18(3")+ 18 12(5") lim

A: Given data is : limn→∞183n+18125n Determine is the sequence divergent or convergent. If it…

Q: Find the limit of the sequence, or show why it doesn't exist, an = n4-(n8-n5)1/2.

A: Given,  Sequence                     an = n4-(n8-n5)1/2

Q: Consider the quadratic function : C→C defined by f(3) = ² + i. (a) What is the long term behavior…

A: Given : A quadratic equation f:ℂ→ℂ defined by f(z)=z2+i. To find : (a) The long term behavior for…

Q: If {a} be a sequence such that lim an +1 an = 1, where | 1|< 1, then lim an = 0.

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Q: help pleae

A: Step 1:   Step 2: Step 3: Step 4:

Q: (b) Give a recursive definition of the sequence {dx},k =1, 2, . .. if (a) dk = 4k – 2; (b) dɛ =…

A: According to the guidelines, I am solving a,b and c part only.But part d can also be solve using…

Q: For each of the following sequences, find the limit and show your reasoning. (-1)" n! (i) lim 2…

A: The objective is to find the limit.

Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

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Q: Find the limit of the sequence an= 3n−4/2n+3

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Q: lim 3n+2 2n + 1 = 3/2

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Q: Does the sequence whose nth term () 2 an n converge? If so, find lim,→ an -

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Q: Give the definition of a subsequence of a sequence Xn.

A: the definition of a subsequence of a sequence Xn.

Q: Suppose the sequence of numbers o, ₁,...,,... satisfies the difference equation 2k+1=0k+ where a and…

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Q: [sqrt(3n+1)] / [ 2 + sqrt(n)] does this sequence converge? or diverge? and why?

A: The given sequence 3n+12+n. We have check whether the sequence is converges or diverges.

Q: If lim(x,) =5100, then (Xn) is bounded. Select one: O True O False

A: 1) Here, lim (xn)=5100 that is finite. That is the sequence xn is bounded. So, the statement is…

Q: Let (a,) be an unbounded sequence and (b„) be a convergent sequence. Prove that the sequence (a,-b,)…

A: In this question, we use the method of contradiction to prove the desired result.

Q: Please give an cxample of a sequence (a,) such that: (a) (an) is not bounded above. (b) (an) is not…

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