What is a monotonic sequence? Under what circumstances does such a sequence have a limit? Give example.

Q: -n +1 lim -n2 +n +2

A: Given to find limn→∞-n2+1-n2+n+2n

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

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Q: 1. Given the sequence defined by 1 3- An а1 — 1, ап+1 - - Explain why the sequence converges. Then…

A: We have to explain the given sequence a1=1, an+1=3-1an converges. Also, find the limit of the…

Q: every convergent cauchy Show that Sequence is but the converse is not true general. in

A: Let, be the convergent sequence which converges to . Since, then, for the given ,

Q: an = Inn √n

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

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Q: 5) Determine whether the sequence converges or diverges. If it converges, find the limit An n +1

A: Given sequence an=n3n+1let  an≥0  and bn≥0  be two sequence  such that an>bnif  bn diverges then…

Q: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

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Q: Find the limit of the sequence (an if it converges; otherwise indicate it diverges. an = (-1)" 5 O5…

A: Given: an=(-1)n5n   To find: limn→∞an

Q: Consider the sequence 6" an 2+7" * Determine if the sequence converges or diverges. If it converges,…

A: Given:

Q: Does the sequence {an} converge or diverge? Explain. Find the limit if the sequence is convergent.…

A: Given query is to find the limit of the sequence.

Q: Explain: e is really the limit of a sequence, and the value usually stated, 2.71828… is a numerical…

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Q: , Find the limit of this sequence, or else prove that the sequence diverges: (1- 3 In n an =

A: ANSWER

Q: Determine the limit of the sequence, or state that the sequence diverges. Show the reason to support…

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Q: an = 2 + (−1)n

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Q: What is an infinite sequence? What does it mean for such a sequence to converge? To diverge? Give…

A: A sequence is an ordered list of objects and can be considered as a function whose domain is the…

Q: Give an example of a bounded sequence that has a limit and an example of a bounded sequence that…

A: To give an example of a bounded sequence that has a limit and an example of a bounded sequence that…

Q: Suppose you know that  {an} is a decreasing sequence andall its terms lie between the numbers 5 and…

A: Given: {an}is a decreasing sequence & all the terms of sequence lies between 5 & 8. To…

Q: 3. Determine whether the sequence converges or diverges. If it converges, find the limit.

A: a sequence {Xn} is convergent if lim Xn tends to a finite value when n approach to infinity

Q: 11. Determine whether the sequence an = 8 + converges or diverges. If it converges, n find its…

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Q: Show whether or not the sequences below converge. If a sequence converges find the limit. Explain.

A: Solution is given below:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (If the…

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Q: Determine whether the sequence converges or diverges. If it converges, compute the limit.    an =…

A: Use ratio test

Q: 1. Let the sequence defined by {(5" +7")*}, be given. Show that the sequence is (a) bounded and…

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Q: Does the sequence a, In (n + 1), converge or diverge? If it converges, findits limit. Give reasons…

A: The given sequence is: an=lnn+1n To determine whether the sequence converge or diverge

Q: Determine whether the sequence converges or diverges. If it converges, find its limit:

A:

Q: For any monotonic sequence, convergence and boundedness are equivalent.

A: First i have written two theorems , just use them say that given statement is  TRUE.

Q: 19. Complete Example 3 by showing that the limit of the sequence is 0.

A: This question is taken from the limits in which we have to verify the given sequence having the…

Q: 3. Explain why the following sequence does not have a limit: a, = (-1)".

A: Solve the following

Q: determine if the sequence is convergent or divergent. If convergent find the limit  an=3(1+2/n)n

A: The nth term of the sequence is    an =  3(1 + 2/n)×n   =  3n + 6    Thus, sequence is  { 6, 9, 12,…

Q: Determine whether the sequence is convergent or divergent. If it is convergent, find the limit. an…

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Q: Give an example of a nondecreasing sequence without a limit.

A: Give an example of nondecreasing sequence without limit.

Q: 3) Does the sequence a, = converge or diverge? If it converges, find the limit of the (7/8)*…

A: given sequence is , an =  1011n 78n+ 1213n   A sequence converges when n→∞    an = 0

Q: Using the definition of limit of a sequence, show that n+1 lim 1.

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Q: Consider the sequence 6" an 2+ 7" Determine if the sequence converges or diverges. If it converges,…

A: Given Data The sequence is an=6n/(2+7n).   Use the ratio test to determine the sequence is converges…

Q: a, = 23+!

A: Sequence and it's it's convergence

Q: Determine whether the sequence (an) is convergent, or divergent. Find the limit if it is convergent.…

A: Consider the given sequence an=21+3nn

Q: Find the limit of the sequence: (;), ÷ (; + -), ; (; + +), E (E )..

A: We have 1112, 1223+24, 1334+35+36, 1445+46+47+48, ... We need to find the limit of this sequence.…

Q: Determine if the sequence is convergent or divergent. If it is convergent, find the limit: an = (1+…

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

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Q: Does the sequence converge? If so, what is its limit? If not why not? ne-n nten n=1

A: 1) The given sequence is;  (ne-n/(n+e-n))infinity n=1. 2) The given series is 2/(-5)n.

Q: Determine whether the sequence an = n° + ... + n4 + n4 n4 converges or diverges. If it converges,…

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Q: Does the sequence {a,} converge or diverge? Find the limit if the sequence is convergent. 5/n an

A: The given sequence is an=5n5/n If limn→∞ an exists and it is finite then sequence an is convergent…

Q: What is a monotonic sequence? Under what circumstances does such a sequence have a limit? Give…

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Q: n! an := 2n+1

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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) < 1, (3/4)n is monotonic decreasing.…

Q: What is the connection between the concept of the limit of a sequence and the limit of the function?

A: Solution

Q: Determine whether the following sequences are convergent or divergent. If a sequence is convergent,…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: What theorems are available for calculating limits of sequences? Give examples.

A: There are six theorems are available for calculating limits of sequence.

Q: Does the sequence {a,} converge or diverge? Find the limit if the sequence is convergent. In (n + 4)…

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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.