n+5 a. (xn) = п-5 n² b. (xn) = %3D п3+1

Q: 2. Determine whether the following sequence converges, and if so, find its limit. (a) nn (b) {n°e-»}…

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Q: {)}. k > 0 is constant number en

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Q: , Find the limit of this sequence, or else prove that the sequence diverges: (1- 3 In n an =

A: ANSWER

Q: (d) 3n 2n + 1 8 n=1

A: We have to show that the given sequence  is convergent.

Q: Find a topic relating to the Boundedness of Convergent Sequences for a final project

A: To Find: A topic relating to the Boundedness of Convergent Sequences for a final project.

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

A: We find the limit of the an th term. limx→∞(an)=limx→∞1+(-1)nn=1+limx→∞(-1)nn=1+0=1

Q: 1. Determine whether the following sequence converges. If so, find the limit. If not, state it…

A: Alternating Series Test Suppose that we have a series ∑an and either an=-1nbn or an=-1n+1bn where…

Q: Determine the convergence or divergence of the sequence whose nth term is An=sqrt(n+2)-sqrt(n). If…

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Q: Suppose that the sequence {an} converges to a, where 0 < a < 1. Prove that the sequence {a}…

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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: lim, 3n+1 3 1/5 7n-3 7

A:

Q: Assume that the recursively defined sequence converges and find its limit. a, = - 12, an - 1 = /24 +…

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Q: + 3n –n

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Q: Assume that the recursively defined sequence converges and find its limit. 24 + 2an - 12, an+ a₁ = =…

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Q: Vn cos(nle") n +1 (n + 1)" (а) ап (b) b, = (c) Cn = 2n sin n nn+1

A: The given sequences area) an=ncosn!enn+1b) bn=(n+1)nnn+1c) cn=2nsinπn

Q: Find the limit of the sequence if it converges; otherwise indicate divergence. an =n - Vn² - 18n 18…

A: an=n-n2-18n

Q: Show that any sequence of positive real numbers either has a subsequence that converges, or else a…

A: We have to show that any sequence of positive real numbers either has a subsequence that converges,…

Q: converges

A: