ii) xn √n-1 √n+1' iii) x₂ = (-1)"+¹ + 1/1.

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: {xn} is a bounded sequence such that all convergent subsequences converge to the same number

A: Every bounded sequence has convergent subsequence.

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

A:

Q: is every cauchy sequence is convergent

A: is every cauchy sequence is convergent?

Q: (1–)" is convergent .The sequence إختر واحدا:

A: Answer

Q: Exercise 5. Prove that a non-decreasing (resp. non-increasing) sequence which is not bounded above…

A: Let an be a non decreasing sequence . ⇒an&lt;an+1  ∀n∈ℕ Since an is not bounded above so for any…

Q: Show X n² n² +1 is a Cauchy sequence using the definition.

A: We have to check weather the given sequence is cauchy sequence or not.

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: 2. Determine whether the given sequence {an} converges or diverges with an as given. In each case,…

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Q: A monotonic bounded sequence .A is convergent .B not convergent .C Oscilating .D none of above

A: Option (A) is correct.

Q: Prove that if a sequence  {an} converges, it must be bounded. Is the converse true as well

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Q: 3/Inn h=3

A:

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: Prove, using the e−N definition of a convergent sequence, that the sequence  (1 + 4n)^2/1 − 3n −…

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Q: Let (an) be a bounded sequence. Define (b,) by bn := sup{an, an+1, An+2;...}. Prove that (bn)…

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Q: Suppose that the sequence {an} is monotone and that it has a convergent subsequence. Show that {an}…

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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: whether the statement is true or false. a) Sequence is convergent if and only if monotone.

A: False

Q: is convergent pounded sequence not صواب ihi

A:

Q: Every convergent sequence is bounded. O True O False

A: Every convergent sequence is a bounded sequence, that is the set {xn : n ∈ N} is bounded. Remark :…

Q: If a sequence is convergent then it is bounded and monotone." Give an example and explain why this…

A: The given statement, "If a sequence is convergent then it is bounded and monotone." is false. Let is…

Q: Show that a convergent sequence is bounded both up and down.

A: Show that a convergent sequence is bounded both up and down.

Q: Prove that a bounded nonincreasing sequence converges to its greatest lower bound.

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Q: 5. Prove that every bounded complex sequence has a convergent subsequence

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Q: Find the limit of the sequence or determine divergence {2n+13-n}

A: Given sequence {2n+13-n}={un} (say)