x = -1/n when n is odd, and an = 1/2" when n is even

Q: Q1/ is the sequence {a,) converge > sin n

A: We have to find given sequence is convergent or not .

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

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Q: If ∑x_n and ∑y_n are convergent, show that ∑(x_n + y_n) is convergent.

A: The objective of this question is to prove that if the series of x_n and y_n are convergent, then…

Q: Prove that the sequence ((-1)")=1 does not converge to any number.

A: Solution :- The given sequence is                          {  an }   =   { (-1)n}  then , we have to…

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. an = + 3 n…

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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: show if it converges or diverges ∑(sqrt(n+1) - sqrt(n))/sqrt(n2+n)

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

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Q: If (an) is a sequence converging to L, prove that (an)=1 converges to L.

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Q: is convergent to

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Q: Is the sequence {n/(n2+1)} convergent? If so, what is the limit?

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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: why sequence Xnk approaches +infinity and why sequence Xmk approaches -infinity. Why would one use…

A: To determine whether the sequence ( n sin(n) ) is divergent and whether the limit approaches…

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

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Q: nsin(4/n) determine if the sequence converges or diverges.

A: I have given the answer in the next step. Hope you understand that

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: What is a sequence that can be graphed that converges to 5?

A: Please find the answer in next step.

Q: If (Xn) is a monotone sequence, then (x,) converges O False O True

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Q: Is {-(n2)} n=1 to infinity, a convergent sequence in R with the usual metric?

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Q: Prove that a convergent monotonic sequence is bounded.

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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: If {A_c} up ∞ down c=1is a convergent sequence , then {1/A_c} up ∞ down c=1 is a divergent sequence.…

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Q: Let (an) be an increasing sequence of real numbers bounded from above and (bn) be a decreasing…

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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)

Q: Show that a convergent sequence is Cauchy.

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Q: Let a (> 1) be an irrational number. Show that the kth convergent of the simple continued fraction…

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Q: (6) Show that the sequence {n} with 1 > 0, n+1 = 2+In its limit. n> 1 is convergent. Find

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Q: Give an example of a uniformly bounded and uniformly equicon- tinuous sequence of functions on the…

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