3. Which of the following sequences are bounded: (i) () (ii) (n+ (iii) (1-) (iv) +1)

Q: The 2 – tail of the sequence Y = (1, 3, 5, 7, 9,... , 2n – 1, . ..) is: O Y = (7,9,..., 2n + 5, ...)…

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Q: 9. Suppose G is the generating function for the sequence 4, 7, 10, 13, 16, 19,..., the find a…

A: The given sequence is 4,7,10,13,16,19,….We need to find the generating function for the sequence of…

Q: The limit of the sequence a.- (1+ (a) - (3) e) (c)e None(e)

A: This is 1 to the power infinity form question so accoding to that I wrote the formula to Solve this…

Q: Which of the following is the generating function for the sequence 5, 5, 5, 5 O A. G(x)=(1-x) 1 O B.…

A: Generating Function: Generating Function is a way to represent an infinite sequence. Consider a…

Q: 29. Let (un) and (vn) be two sequences defined by uo = 1, vo = 2 and for all n EN: Un+1 = 3un + 2vn…

A: Given two sequences (un) and (vn). This question has three subparts. The solution is given below.

Q: Consider the set of sequences X = {(xn): xn € {0,1}, n € N} and Y = {(x₂) € X | x₂ = 1 for at most…

A: There are two sets X and Y of sequences such that            X= {(xn) ; xn∈{0,1} , n∈N }…

Q: 2. Find the closed form for the generation function for the sequences (i) 2, -2, 2, -2, 2, -2, - - -…

A: The closed form for the generation function for a sequence is used to define the general term of a…

Q: Which one of the sequences below is divergent? 2n? 3n + 17 2n 3n + 5J 2n n +n +1 D {2-} D

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Q: (ii) If (sn) is an unbounded decreasing sequence, then lim så -∞

A: Given that {sn} is an unbounded decreasing sequence. To show :- limn→∞sn=-∞

Q: 2. an+1 sequence? for an Show that the sequence in Q1(a) is eventually strictly decreasing by…

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Q: 3 4 N + 1 5) Show that the sequence 7 2N + 1 is bounded and monotonic.

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Q: Find the closed form for the generating function for the following sequences: a) (9,0), (9,1),…

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Q: 12. Suppose the sequence ao, aj, a2, a3, ... is defined as follows: ao = 0, aj = 1, and for n > 2,…

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Q: 3. Find the generating function in simplified form for each of the sequences (b) 0,0, (), 2(),…

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Q: 8. Consider the sequence {an} such that an+1 = -3 – 2an. Then lim an = -1.

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Q: 6. The sequence (xn) = (3,3,3,3, ...) is .. a) not Cauchy b) unbounded c) divergent d) convergent

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Q: Consider the set S which includes the sequence {(1,),(¿, ) ; (¿, 1) ; ...; (0, 1)}. Now consider the…

A: (a) Given S=1,12,12,23,13,34,...,0,1. The members of S heap or cluster near 0,1 and every…

Q: (c) A non-constant function f : [0, 1] → R such that f(x) > 0 for any x e [0, 1]I f(x)dx = 0. Give a…

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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: Find the closed form of the generating function for the sequence 2,4, 8, 16, 32, ...

A: Generating Function: Let a0, a1, a2, a3, a4, .....be a sequence of real numbers denoted as an Then a…

Q: 5 Fn+1 3 F,. Compute R6 Define a Sequence R,

A:

Q: 1. Let a, = 1 and an+1 = 1+ 1+an (a) Find the first six terms of the sequence {an}. (b) Prove that…

A: As you asked multiple sub parts so I answered 1st three subpart.

Q: 1.4 Consider the set S which includes the sequence {(1,),(;, ) ; (§, 1) ; ...: (0 1)}. Now consider…

A: Solution: (a) The set S is S=1,12,12,23,13,34,...,0,1 Clearly, the set S is the collection of open…

Q: For each of these generating functions, provide a closed formula for the sequence it determines. a)…

A: (Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Determine which of the following sequences are monotonic. Then guess their limits (where applicable)…

A: First let's discuss what is monotonic sequence in a layman language. monotonic sequence is a type of…

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.