3. Let a₁ = = 1, an+1 = √2an for ne N. Prove that the sequence {an}_1 is convergent and find its limit.

Q: Let x₁ = √2, and x1 Xn+1 = 2 + √√xn, n = 1, 2, 3, .... Prove that the sequence {n} converges, and…

A: Let  and To Find:Prove that the sequence is monotonically increasing and bounded above also shows…

Q: Prove that if {xn} is a sequence such that 1+ n |æn| < for all n E N, 1+ n2 then the sequence {xn}…

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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: Find the limit numbek of the fallawing Sequencer er divergente and which of them is convergent 4-…

A: To find the convergence of the sequence and obtaining the limit

Q: 7. let (an)neN be the sequence defined as a, = + (i) Find the limit of an (ii) justify your limit in…

A: Limit of the sequence and and jestification of the sequence.

Q: 50. A sequence a, is defined inductively as a, = v3 and a41 = /3 + a, ,Vn 2 1. Find the limit %3D of…

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Q: If {f} converges in the mean squa

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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: Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i.…

A: Bounded sequence and sum of bounded sequences.

Q: 1 Let xn=G, 2+-), nEN be a sequence in R?, then lim x, .A (0,2) .B [0,2] .C (2,3) .D (0,2]

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

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Q: 23. an n √n² +1

A: We take n common from the root and then apply limit to find the vale of limit.

Q: 20

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Q: The first term of a converging sequence {an} is given by, a1 = 0 and the remaining terms can be…

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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: 12 Exercise 6. We are given a > 0, and the sequence x, defined recursively as follows: x₁ > √a, Xn+1…

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

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