1) Using the appropriate formula, find the 17th term of the sequence 7, 4, 1,.... 2) If h is defined by h(x) = |x| + 2, a) What is the range of h if the domain of h is the interval [-8,2)? b) What is the range of h if the domain of h is the set of negative integers?

Q: 1-Let B be the set of all infinite sequences over {0, 1}. Is this set countable or not, prove it?

A: Please post the multiple parts separately.Here I answered the 1st question as per our policy.

Q: Use any method to prove that if X = (xn) is a Cauchy sequence of real numbers, then () is also a…

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Q: 8. Give the first five terms of the following recursively defined sequence: a1 = 2. and ar = ax-1 +…

A: Recursive definition of a sequence is one in which one term can be determined using previous terms…

Q: The sequence {4 - } is bounded. Select one: O a. None of these

A: Solution of the problem as follows

Q: Let Fn be Fibonacci sequence. Prove that:

A: By the definition of the Fibonacci sequence, Fn+2=Fn+1+Fn and the Fibonacci sequence is satisfied…

Q: . Suppose real sequences (S,) and (t,) are bounded. (That is, that their ranges are bounded sets.)…

A: Given the real sequences sn and tn are bounded. We have to show that The sequence given by sn + tn…

Q: Prove that a sequence in ℝ can have at most one limit

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Q: II. Prove if X and Y are the sequence of real number and converges to x a real number then product…

A: Given that X and Y are the sequence of real number And X and Y converges to x a  real number. The…

Q: Let a, be the nth term of the sequence 1,2,2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,6,…

A: Let, the sequence be an Here, a0=1,a1=a2=2,a3=a4=a5=3, and so on.

Q: Let E ⊆ (Real Number) and E does not equal ∅.  Prove if E is compact then every sequence in E has a…

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Q: Suppose we have a sequence of non-negative real numbers such that each element is strictly less than…

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Q: Consider the sequence {. n+2 1. Determine the number of terms that are not within ɛ = 0.0002 of 3.…

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Q: a) Show that the sequence a, = (-1)" +- does not converge. b) Let b, be a sequence such that for all…

A: Given the sequence an = ( -1 )n + 1/n . It has two subsequences a2n = 1 + 1/n converging to 1 and…

Q: Among these statements, which are true and which are false There is a sequence with an infinite…

A: 1. TRUE x(n)=1-((-1)^n) which has Range ={0,2} and for every alternate terms we have infinite zeroes…

Q: A sequence s, is said to be bounded above if there is some number N such that.... .a Sn =N .b .C…

A: Option d is correct.

Q: Prove {3n/(3n-1)} n=1 to infinity, is a decreasing sequence in R.

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Q: C) Prove that a Cauchy sequence of real numbers is bounded.

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Q: 3. Use the definition of limits of sequence to give a formal proof of lim (√n+1-√n) = 0.

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Q: Find the generating function of the sequence {a;}k20 defined by ak = -3 if k even; a = 3 if k odd.…

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Q: Let {an} be a real number sequence. Prove that                             {an}= {1+(1/2n)}…

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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: Define the sequence {an} as follows: aj = 2 an = an-i + 2n for n > 2

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Q: Evaluate the limit of the sequence or state that it does not exist. an = n - √(n2 - 1)

A: Given sequence is an=n-n2-1.

Q: Let an be the nth term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,…

A: The given sequence is 1,2,2,3,3,3,4,4,4,4,..., The first integer 1 occurs in first position. The…

Q: consider the sequence  1, 1/2 ,1, 1/3 ,1 ,1/4, 1,.........  determine the limit superior and limit…

A: Given sequence 1, 1/2 , 1 , 1/3.. The limit superior is 1. As every number of sequence < 1+k for…

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

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Q: If (xn) is a Cuachy sequence in R, then it is unbounded. Select one: OTrue OFalse Every sequence of…

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Q: 3. Prove that if (a, } and (b,} are Cauchy sequences of rational numbers satisfying lim (a, - b, = 0…

A: 3.

Q: Prove or disprove that if a sequence {x,} satisfy x,+1 – xn → 0 then it is Cauchy

A: We have to solve given problem:

Q: (a) Define a sequence by ai = 7, and ak+1 = Vak for all k > 1. Does ak converge or diverge? Explain.…

A: We will be using some simple and well known results of series to arrive at the final solutions

Q: The Fibonacci sequence (fr) := 0, 1, 1, 2, 3, 5, 8, ... is an example of a ecursive sequence with…

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Q: Prove { (8n-7)/n} n=1 to infinity is an increasing sequence.

A: If we take the sequence as {Un}, and if we can able to show that for all n=1,2,3, ...  Un+1>Un…

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: 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: Show that the set of limit-points of a sequence is a closed set.

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Q: 2. Suppose x,, X2 , X3 ..... Isa sequence defined by x, = 2, X2 = 4, bk-2 + 2bk-1 for all integers k…

A: Since you have asked multiple questions, we will solve the first question for you. Note:- In…

Q: 9. Let {xn}, be a sequence of real numbers. What does the boundedness of this sequence mean?

A: Given xnn=1∞ is a real sequence.

Q: 5. Find the limit of the sequence 3. an ), n = 1,2, 3, --. 3JT

A: Explained below

Q: Evaluate the limit of sequence ak  = k-1/k-2

A: We have to find limit

Q: Suppose that b1, b2, b3, . . is a sequence defined as = 12, b = br–1 + b-2 for each integer k > 3.…

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Q: Consider the sequence  1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, ... Determine the limit…

A: Here sequence is given derive from.this

Q: Evaluate the limit of the sequence or state that it does not exist. an = (π)/(2) - tan-1n

A: To evaluate the limit of the sequence an=π2-tan-1n

Q: Prove that the following sequence is cauchy sequence by definition (xn) = Vn +1– Vn Hint :…

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Q: 5 terms of the sequence defined ce relation. That is, find a closed

A: Introduction: The value of n should be organised and precise, as in the Simplest form. In the…

Q: Let an be the nth term of the sequence 1,2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,…

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Q: Question 3. Use the method of finite-differences to find a closed-form expression for the sequence…

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Q: True or False. There exists a sequence (an) such that for every k ∈ N and every ε > 0, the interval…

A: There exists a sequence (an) such that for every k ∈ N and every ε > 0, the interval (k − ε, k +…

Q: 4. Define a sequence by an+1 = -an?, with -1 < ao < 0. Prove that {an} is increasing and bounded…

A: Consider the terms of the sequence put n=0 a1=-a02 here -1≤a0&lt;0 So -1≤a1&lt;0 but certainly a1≥a0…

Q: Show that the real sequence ( 0,-1,2,-3 , .... , (-1)nn, .... ) where n is a value from the set of…

A: Consider the given sequence,

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.