Question 2 10 Determine the boundedness and monotonicity of the sequence with an = п a) Ononincreasing; bounded below by 0 and above by 10. b) decreasing; bounded below by 0 and above by 10. c) increasing; bounded below by 0 and above by 10. d) decreasing; bounded below by 1 and above by 10. e) Onondecreasing; bounded below by 1 and above by 10.

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: Let (a,)nen be a bounded sequence and let b= sup{ a, : nƐN } Show that if b is NOT a member of { a,…

A:

Q: EXAMPLE 8, Does the sequence whose nth term is n п + An n 1 - converge? If so, find lim,»oan.

A:

Q: 4*++3" Consider the sequence a, = (a) Is the sequence monotonic pr non-monotonic? If it is…

A:

Q: What is the closed form for the infinite geometric sequence beginning  4,2,1,1/2 where the first…

A: Given :The infinite geometric sequence : 4, 2, 1, 12, ..

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim Sn = .…

A: Limit of a sn

Q: What is the correct answer to guess a formula for tn as a summation written in expanded form, and…

A:

Q: Find the limit of the sequence using L'Hôpital's Rule. b, = BVñ in(1 + 4) lim b in 123 Tutorial II

A:

Q: In the given question as follows , determine whether the sequence with the given nth term is…

A: Consider the following nthterm of the sequence an=ne-n2  A sequence an is monotonic when its terms…

Q: `11,  Find a function  f(n)  that identifies the nth term  an  of the recursively defined sequence,…

A: The solution is given below

Q: Show directly from definition that if a, is a positive real sequence with lim a, = 0 and lim f(r) =…

A: Solve.

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: Prove that there is no hooked Skolem sequence of order n= 8.

A: To Prove - Prove that there is no hooked Skolem sequence of order n = 8.         Theorem used - A…

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

A:

Q: 3.) Determine whether the sequence is monotonic and whether it is bounded. sin /n

A:

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: determine whether the sequence is monotonicand whether it is bounded. an =(2n + 3)!/(n + 1)!

A: To find the sequence is monotonic or bounded. Consider

Q: The Fibonacci number is a sequence which is described explicitly by Fn = Fn-1 + Fn-2-

A: Given statement is The Fibonacci number is a sequence which is described explicitly by  Fn = Fn-1 +…

Q: 4. Give a recursive definition of the sequence an if an = n(n+1), where n = 1, 2, 3, ... %3D

A: We have to give a recursive definition of the sequence an where an=  n(n+1) for n= 1,2,3,....

Q: Looking for some help in proving this sequence is Cauchy.

A:

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: 2) Show that the sequence defined recursively by 3 4 An aj = 5 аn+1 satisfies 2 < an < 5 and is…

A:

Q: Every bounded and monotonic sequence is divergent. Select one: O True O False

A: We know that monotonic increasing                 (or decreasing) sequence which is bounded above…

Q: What are the first five terms of the sequence defined over the natural numbers with the explicit…

A:

Q: Find the limit of the sequence as n approaches infinity: In – 8 an = 9п + 1

A:

Q: Which of the given infinite sequences is both an increasing and a finite sequence for every n≥1?

A: a sequence is increasing if an+1 ≥ an for all n ≥1   We have to check one by one which one…

Q: Is the limit of the ratio of any two successive increasing terms of the Fibonacci sequence.

A:

Q: 4 – 7n6 an- nº +3

A:

Q: Calculate, to four decimal places, the first ten terms of the sequence. an = 1 + (-) %3D

A:

Q: (a) Let {n} be a sequence such that there exist A> 0 and c € (0, 1) for which n+1- n ≤ Ac" for all…

A: As per the policy, we are solving first question. Please repost the question and specify which…

Q: Suppose 1 aj = 2 3 4 5 1 az = , as ', a5 = 2 – 2 3 3 4 - 4 5 - 6. 6. | a) Find an explicit formula…

A: Given: a1=12-12, a2=23-13, a3=34-14, a4=45-15, a5=56-16, For (a), So, now the explicit formula is…

Q: Supposed vn =17-n2  is the explicit specification for a sequence. How many values of n (positive)…

A: Given: Vn=17-n2

Q: Determine if the sequence is monotonic and if it is bounded. n! 5n

A:

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: how that the sequence (1 – (-1)" +1/n) is divergen

A:

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim S, = 2…

A:

Q: determine the limit of the sequence or show that the sequence diverges.

A:

Q: Does there exist an example?or show that none exists . A sequence that tends to infinity and has a…

A:

Q: 3" 1 Determine whether this sequence is monotonic, and whether it is bounded above and below: a, =…

A: Consider the sequence an with an=3nn+1!. Replace n by n+1 in an=3nn+1! and obtain an+1=3n+1n+1+1!.…

Q: The generating function of the sequence 5,5,5,5,5 is 1-x° (1-x) 1-5x° (1-x) 1- 125x (1-x) 1-3125x…

A:

Q: Verify that the ratio of any two consecutive numbers of Fibonacci sequence starting at 3 converge to…

A: First we will give definition of fibonacci sequence and list the 10 terms of the sequence

Q: C. Show that any sequence of positive real numbers either has a subsequence that converges, or else…

A: Proof of theorem

Q: 6. When a, = n(-1)", determine whether the sequence {a„} is increasing, %3D decreasing, or not…

A: We have been given the sequence an=n(-1)n

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: The generating function of the sequence 5,5,5,5,5 is 1-x5 O (1-x) 5 1-5x° O (1-x) 1-125x5 (1-x)…

A: We need to find the generating function of the sequence 5,5,5,5,5.

Q: Consider the sequence a, = 4+1+3" 4" (a) Is the sequence monotonic pr non-monotonic? If it is…

A: (a) an = (4n+1 + 3n)/4n            = 4 + (3/4)n     As (3/4) &lt; 1, (3/4)n is monotonic decreasing.…

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: What theorem sometimes enables us to use l’Hôpital’s Rule to calculate the limit of a sequence? Give…

A: The theorem which enables us to use L'Hospital’s Rule  is,

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.