Prove {52 + 11/n} n=1 to infinity converges to 52 using the definition of a convergent sequence.

Q: True or false: Suppose {n} is a sequence of real numbers, and I is a real number such that for every…

A: Here the above mentioned statement is true.

Q: A convergent sequence is bounded. A True B False

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Q: (c) Is the sequence {n-1}, a Cauchy sequence? Explain your answer. (d) Suppose that (a) is a…

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Q: (-1)"n For positive integer n, let an = 3" Determine whether the sequence {a,} is convergent.

A: Determine whether the sequence is convergent ?

Q: {)}. k > 0 is constant number en

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Q: Show that the sequence defined by  a sub 1= 1  and  a sub n + 1 = 3 - (1/ a sub n) is increasing and…

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Q: Suppose that {an}----->a, convergent real number sequence. Prove that {can}---->ca, for every c…

A: Suppose that {an}----->a, convergent real number sequence. Then, We have to prove that…

Q: is every cauchy sequence is convergent

A: is every cauchy sequence is convergent?

Q: Using the definition of convergent sequence, prove -2 3 4 - 2n lim n∞ 3n+3

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Q: Show X n² n² +1 is a Cauchy sequence using the definition.

A: We have to check weather the given sequence is cauchy sequence or not.

Q: The greatest lower bound for the sequence {0.1,0.01,0.001, 0.0001, ...} is

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Q: 2. Determine whether the given sequence {an} converges or diverges with an as given. In each case,…

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Q: Prove, using the e−N definition of a convergent sequence, that the sequence  (1 + 4n)^2/1 − 3n −…

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Q: If (an) is a sequence converging to L, prove that (an)=1 converges to L.

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Q: This is a sequence, which test should I use and is it convergent/divergent? Explain. {(-1)n (n+1),…

A: This is a sequence which test should I use and is it convergent/Divergent? {(-1)n(n+1)!/3n!}…

Q: Rico spent $87.00 to go to the movies on Friday night. He paid $25.75 for popcorn and drinks and…

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Q: Is the sequence {n/(n2+1)} convergent? If so, what is the limit?

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Q: x = -1/n when n is odd, and an = 1/2" when n is even

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Q: Suppose that the sequence {an} is monotone and that it has a convergent subsequence. Show that {an}…

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Q: Use iteration to guess an explicit formula for the sequence defined by an = an-1 + n for all…

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Q: Determine the convergence or divergence of the sequence whose nth term is An=sqrt(n+2)-sqrt(n). If…

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Q: Suppose that the sequence {an} converges to a, where 0 < a < 1. Prove that the sequence {a}…

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Q: whether the statement is true or false. a) Sequence is convergent if and only if monotone.

A: False

Q: Solve the Lucas sequence L_n = L(n-1) + L(n-2), n ≥ 3; L_1 = 1, L_2 = 3.

A: The objective of the question is to solve the Lucas sequence. The Lucas sequence is a sequence of…

Q: What is a sequence that can be graphed that converges to 5?

A: Please find the answer in next step.

Q: Find n such that the geometric sequence becomes less than 1: {400, 240, 144, 86.4, ...} n3D

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Q: (b) Decide the convergence or divergence of the sequence a = √8 and an+1 √8+ an.

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