QUESTION 1 n in{1+4). The sequence {an} where converges and has limit | = TTTT Paragraph Arial 3 (12pt)

Q: Give an example of a bounded sequence {a„}_1 having exactly 2 limitpoints.

A: we have to find a sequence such that it has two limit points.

Q: 1 Prove that if a sequence {a„} converges to a, then the sequence {[an]} converges to |a|. Find…

A: Suppose {an} converges to a. Prove that an converges to a. Also, check the converse is true.

Q: If the sequence {a}, is convergent, then the sequence {x} defined by a₁+as+as++an-stan is also…

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Q: 2) Show that the sequence defined recursively by 3 4 An aj = 5 аn+1 satisfies 2 < an < 5 and is…

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Q: an n In n en (domain n ≥ 1)

A: Given that an=nln(n)en We have to find it's limit when n tends to infinity.

Q: (-9)"+1 Let an 10n Determine whether the sequence {an} is convergent or divergent. If it is…

A: an=(-9)n+110n A sequence is convergent if value of limit is define and finite as n approaches to…

Q: 19. an = IN 2 τη

A: The sequence is given as an=12-n

Q: n=1 m sup,+∞ an = (lim infn an)+2. %3D n-00

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Q: 6n Determine if the sequence an 4(-1) converges or diverges. If it converges, compute its limit. If…

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Q: A sequence {an} is defined by a1 = 2 and an+1 =3(1+an)/5+anfor all n ∈ N. Find the limit of such a…

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Q: Determine if each sequenceconverges or diverges. If it converges find the limit. Clearly explain…

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Q: 10) Does the sequence an = √n² + 3n - n converge or diverge? Explain

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Q: Find a sequence of real numbers {a;} such that lim a, does not n-00 xist, but it has 3 subsequential…

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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: Use Squeeze Theorem to find the limit of the sequence {4n/n!}

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Q: Let (an) be the sequence defined recursively by a₁ = √3, an Prove that (an) is bounded. = √2an-1 +3,…

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Q: 6. Consider the sequence defined recursively by 1 2 an+1 = an + N an If ao = 1, does the sequence…

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Q: Which of the following sequences are bounded? Select all such sequences. X That's not right. 6n…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.