1. For each of the following sequences, (i) Compute lim sup and lim inf. (ii) Determine whether the sequence has a convergent subsequence. (iii) Write down a convergent subsequence in case there is one. bn = ((-1)" - 2)n, an = (1-(-1)")n 2n - 9 2n + 3 3n + 4 Cn = (-1)";

Q: Find the limit of the following sequence or determine that the sequence diverges. {((2n3 + n) tan-1…

A: If the limit of the sequence does not exists, we say the sequence is diverges.

Q: Determine the limit of the sequence a, (-1)* 1 1 2 2 - 1 Divergent

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Q: 1. Give an example of a sequence {an} where lim(an+2 – an) = 0 but {an} is divergent.

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Q: Find the first four terms of the following recursively defined sequence. tk = tx - 1+ 2tx - 2, for…

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Q: Determine the generating function for the following sequence: (),-), (2),,(-1)" (a),.. where a is a…

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Q: Let =-7 and I+(3, +4) for all integers n2 1. (a) Show that xnS 2 for all n. (b) Show that (x,} Is an…

A: All proofs are easily only  a) proved using induction  b) proved using definition c) find using a…

Q: (b) Give a recursive definition of the sequence {dx},k =1, 2, . .. if (a) dk = 4k – 2; (b) dɛ =…

A: According to the guidelines, I am solving a,b and c part only.But part d can also be solve using…

Q: 2. (Recursively Defined Sequences). (i) Study the following program for a scientific calculator for…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Suppose you want to type sequences of vowels (that is, the letters a, e, i, o and u). However, the e…

A: Given  the number of sequences of length   (i) Find (ii) Write a second-order difference equation…

Q: 2. Write the first five terms of of each recursively-defined sequence. t(1) = 3t(n + 1) =- 2-t(n)…

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Q: 1. Let (n) be an increasing sequence of positive real numbers and define the sequence (yn) as…

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Q: Use the definition of the limit of a sequence to show that: mm ( 2²2 +²13) = 1/21 n (b) lim (√n² + 1…

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Q: (a) (b) Find the limit of the following sequences or show why they diverge. In(5n6) 1 7n-1 +n8 8n³ +…

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Q: (c) Let (sn) be a sequence of negative numbers (sn <0 for all n E N). Prove that lim 8, = -00 if and…

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Q: Evalu

A: (a)

Q: A sequence is defined by f(1) = 3 and f(n) = 2. f(n –1) for n > 1. Which of the following statements…

A: Here given  f1=3,fn=2·fn-1

Q: Find a function  f(n)  that identifies the nth term  an  of the recursively defined sequence, as  an…

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Q: Let an be a sequence defined by a1 = 0 and a2 = 1 and for n > 3 an = (n – 1)(an-1+an-2). %3D

A: Here, the terms given in the series are, a1=0,a2=1an=n-1an-1+an-2 Calculate the third, forth and…

Q: Suppose that the sequence x0, x₁, x2... is defined by xo = 3, x₁ = 6, and xk+2=-6xk+1-5xk for k20.…

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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 {10, -2, ) Find a formula for the general term an of the sequence, assuming…

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Q: Give the definition of a subsequence of a sequence Xn.

A: the definition of a subsequence of a sequence Xn.

Q: Find the sequence {an}nzo for the generating function G(x) = (x + 2)². ao = 4, a₁ = 4, a2 = 1 and an…

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Q: Find explicit formulas for sequences of the form a1, a2, a3, . . . with the initial terms given…

A: Given that the sequenceAnd  To find the nth terms

Q: (c) (d) In n (−1)” +00 n=1 2n³ 3 n + +1 +00 n=1 n

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