A sequence {an} is bounded below and nonincreasing. Does {an} converge or diverge? Use a graph to support your conclusion.

Q: Determine whether the sequence is convergent or diver- gent. If it is convergent, find the limit. 1…

A: Given:To determin whether an=13n4 is convergent or divergent

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: an=2n+3 apply limit n→∞ if limn→∞an=L then the sequence is converges and if limn→∞an=∞ then the…

Q: determine the limit of the sequence or show that the sequence diverges. an = 21/n2

A: Given that, an=21n2

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: Find the limit of the sequence whose nth term is an = In(2n + 1) or show the sequence diverges. Be…

A:

Q: Determine if the sequence is bounded and if it is monotonic. Determine if the sequenc converges and…

A: The given sequence is: an=(-1)nn100 Now, the terms of the sequence are: a1=-1,a2≈1.00,…

Q: Determine whether the sequence is convergent or diver- gent. If it is convergent, find its limit.…

A: We have ∑n=0∞an=∑n=0∞9n+110n=∑n=0∞9·9n10n=9∑n=0∞9n10n=9∑n=0∞910n=9·Sn

Q: Find the limit of the sequence if it converges; otherwise indicate divergence. 5+(-1)n an= Diverges

A: The given limit of the sequence is an=5+-1n5. The above sequences have two repeats values for all…

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: We have given a sequence; an =(n + 1)!/ n!

Q: Determine the convergence or divergence of sequence with the given nth term. If the sequence…

A: According to the guidelines issued by the company We are supposed to answer only first three…

Q: is every cauchy sequence is convergent

A: is every cauchy sequence is convergent?

Q: determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: Using Desmos graphing calculator, I have got this graph.

Q: Determine whether the sequence is convergent or diver- gent. If it is convergent, find the limit. n³…

A: To Determine: find whether the sequence is convergent or divergent ,if it is convergent find the…

Q: 1 {4 +

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Q: Indicate if the following statement is TRUE or FALSE. Briefly justify your response with an…

A: To indicate whether the following statement is TRUE or FALSE.If a sequence has a bounded…

Q: Determine if the sequence is convergent or divergent. If it converges, find the limit.

A: Given,  nln2+1nn=1∞ We know that ,an=nln2+1n

Q: anz3

A:

Q: Find the limit of the sequence if it converges; otherwise indicate divergence. an in 1 0. 7.…

A: an=7n.nn

Q: 5. Determine whether the infinite sequence converges or diverges. If it converges, find the limit.

A: Find the attachment

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: Solution: The objective is to determine whether the given series is convergent or not

Q: (1.1.1-4-3-3-4-6,...} 1, 3, 2, 4, 3, 5, 4, 6, { {

A:

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: Does the sequence whose nt" term is an converge? If so, find lim an. n-00

A:

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

A:

Q: 5* Determine whether the sequence defined by a* %3D 8* +1 converges or diverges. If it converges,…

A:

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (-1)"

A:

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: Given: an=n-2!n! for this first we simplify nth term of given sequence, then find sum till infinite…

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

A:

Q: 4. Give an example of an unbounded sequence that has a convergent subsequence.

A: If a sequence is not bounded, it is an unbounded sequence.  .Now we will give the example to the…

Q: The nth term of sequence is determine whether the squence converge or diverges . If it converge find…

A: The nth term of the sequence is determining whether the sequence converges or diverges. If it…

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

A: Please find the answer in next step.

Q: If it is convergent, fond its sum

A: Apply the identity Then,

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: The given sequence is an = (3/2)n A sequence an is monotonic when its terms are non-decreasing…

Q: 3. Show that the sequence ɑn 1+ is a Cauchy sequence. Hint: Every convergent sequence is a Cauchy…

A:

Q: Show that a convergent sequence is bounded both up and down.

A: Show that a convergent sequence is bounded both up and down.

Q: Does the sequence whose nth term () 2 an n converge? If so, find lim,→ an -

A:

Q: Prove that a bounded nonincreasing sequence converges to its greatest lower bound.

A:

Q: Determine whether the sequence defined by 1/x converges or diverges. If it converges, find its…

A: The given sequence,   an=1+8n1n

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

A:

Q: (-1)-', in a, 3D п? +1

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Q: Find the limit of the sequence if it converges; otherwise indicate divergence. an = (-1)" |1- 1 3 O…

A: we have  an=(-1)n1-3n

Q: f) {1,0,–1,1,0, –1,1,0,...}

A:

Q: b) Show that sum of two unikormly convergent sequence is uniformly convergent.

A:

Q: Determine the convergence or divergence of the sequence with the given nth term. If the sequence…

A: We will use complementary pair of subsequence to determine the convergence of sequence .

Q: 1) Datermine whether the sequence 15375' is convergent or divergent.

A: Since you have asked multiple questions in single request so we will be answering only first…

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

A:

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

A: Divergent test: If limn→∞an≠0 then ∑an is divergent.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. an = 4 +…

A: A sequence converges if it is finite when n is very large (infinite) , Diverges if limit is infinite…

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence…

A: This is a problem of sequence and series.