Establish the convergence and find the limits of following sequences. *[(+] [-] [0) "0-47

Q: If ( a n) is a sequence that diverges to ∞, prove that Iim n --> ∞ (1/a n) = 0

A: Assume that the sequence an diverges to ∞. That implies, limn→∞an=∞.

Q: 2. Let an be the sequence defined inductively by a₁ = 2 and an+1 == 1/2 (a₁ + ²2² ). an (a) Prove by…

A: a. By induction, we can conclude that an € [1,2] for all  n € N.b. It is proven that an2 >= for…

Q: Let (2) be a bounded sequence. Prove that if (en) is monotonically decreasing then it con- verges to…

A: To prove that a bounded, monotonically decreasing sequence {xn​} converges to its infimum, we need…

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

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Q: 4 – 7n6 an- nº +3

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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: 3. Prove that the sequence with nth un (a) is monotonic increasing, (b) is bounded above, (c) is…

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Q: Consider the sequence  1,1/2,1,1/3,1,1/4,1, ... Determine the limit superior and limit inferior of…

A: Given sequence is  1,12,1,13,1,14,1,....... By observation , it can be seen clearly that 1 repeats…

Q: 2. Let (an)1 be a sequence of integers. Prove that (an) converges if and only if there exists a…

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Q: In(n) n a. Calculate the first 10 terms of this sequence. Based on these calculations, do you think…

A: As per the question we are given a sequence as : ln(n)/n And we have to : Calculate the first 10…

Q: Find the limit of the sequence {(₁+ 3 n+ 5 2n S

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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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