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

Q: Determine whether the sequence is convergent or divergent.

A:

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: 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: The sequence with general term an = (-1)" is divergent. True False

A: The given sequence is divergent.

Q: Determine if the sequence 1+ 3n is convergent or divergent.

A:

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: Find the limit of the sequence if it converges; otherwise indicate divergence. 7n in an

A:

Q: 1 {4 +

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Q: Determine whether the sequence diverges. If it converges, find the Converges cr An- cos ( Pie, aiso…

A: To determine whether the below sequence converges or diverges. an=cosnπn+1

Q: Find the limit of the sequence if it converges; otherwise indicate divergence. an=3-n 3 3. Diverges

A: Given: an=3-n

Q: In the given equation as follows, determine the convergence or divergence of the sequence with the…

A: given,        an=-13n

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

A:

Q: Determine whether the following sequence converges or diverges. Inn | In(2n)

A:

Q: Choose the true statements about a convergent series.

A:

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: an = −3−n We need to determine the convergence or divergence of the sequence with the given nth term

Q: Give an example of a nonincreasing sequence with a limit.

A: The nonincreasing sequence is a sequence {An} of the real numbers that never increases that is An+1…

Q: A monotone sequence is convergent.

A: 1) If f is continuous on A then fn is also continuous  on A So The statement is true

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

A:

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

A:

Q: Determine whether the sequence {(3" + 5")/"} is convergent or not.

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: Is the sequence divergent or convergent? If it’s convergent, evaluate

A:

Q: Prove that the sequence (an) = (-1)"+' does not converge to any real number. %3D

A:

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

A: To determine the provided nth-term of the sequence an=(n-2)!/n! is convergent or divergent and also…

Q: 00 Ink

A:

Q: 3- (4z-5)" 5"

A: Given: ∑n=0∞4x-5n5n

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: Determine the limit of the sequence or show that the sequence diverges. If it converges, find its…

A:

Q: In 3n an = In 5n

A:

Q: Does the sequence{an}converge or diverge? If it converges, what does it converge to?If it diverges,…

A: Given, an=nln(n)

Q: (-1)-', in a, 3D п? +1

A:

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

A:

Q: Suppose SELECT ALL A) sometimes converges depending on the sequence, a(n) B) lim a(n) # 0 never…

A: Given that, limn→∞a(n)≠0 then we have to find ∑n=1∞a(n) is convergence or divergence or depends.

Q: Determine whether the real sequence of convergent or divergent sequence. n+3 converges by using the…

A: This is a problem of sequence.

Q: Find a convergent subsequence of the sequence {(-1)" (1 – 4)}, -

A: We need to find a convergent subsequence of {(-1)n(1-1n)}n=1∞.

Q: 4. Determine if the sequence is bounded and if it is monotonic. Determine if the sequence converges…

A: This question is related to sequence and series.

Q: find the limit of the sequence and find if the sequence converge. Show calculations.

A: Consider the limit 6ne−n

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 {√ n+2 - √ n+1} is convergent or divergent

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

A: This is a problem of sequence and series.

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.