3) Justify whether the sequence converges diverges or a-an. 2-n こうe abicai b- an =(-1)"

Q: The sequence (tanh n) converges to2 Select one: True O False

A: To find the convergence of sequence

Q: Show that the sequence {b,}, where b, What can you say about any sequence with these two properties?…

A: we say any sequence which  eventually increasing as well as bounded above, it converges. It is also…

Q: Find the general term of the sequence, starting with n=2 and test for convergence. (/2 – J5) (3-VA)…

A:

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

A: Given that, an=21n2

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: 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: Show directly from the definition that the following is not Cauchy sequence. (-1)"\ n +

A: This is the question from the sequence and series.

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

A:

Q: Does the sequence whose nth term is a, = () converge? If so, find lim an. n+1\n

A: If ∑an converges than limn→∞an=0.

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

A:

Q: Cn = Jns -Jn? 13 ニ

A: The given sequence is an=n3-n2.

Q: Explain why you think the sequence 1-(-1)" con converges to a finite number or n+1 diverges. If the…

A:

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: does the sequence whose nth term is an = ( n+1/n-1)n converge? If so, find lim n→∞  an.

A:

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

A:

Q: If the sequence converges, enter its limit. If it diverges to oo, enter "infinity". If it diverges…

A:

Q: The sequence (tanh n} converges to2 Select one: True O False

A: This sequence converges to 1.

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: If E-ja, is a convergent series of nonnegative numbers, can anything be said about Ea,/n)? Explain.…

A:

Q: Determine whether the sequence {√n+2−√n+1} converges or diverges.

A: To check for the convergence of the given sequence, we find the following limit: To calculate the…

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

A:

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

A:

Q: Show if the sequence converges or diverges using  L'Hôpital's rule…

A: A sequence is said to be converge if its limit  exists, otherwise diverges.L'Hospital rule:- If…

Q: Prove that the sequence defined by a1 = −3 and an+1 = (1/4)(2an-1) converges. Then prove that it…

A: Given sequence is defined by a1=-3, and an+1=142an-1  ,n>1 We have to prove the sequence…

Q: Determine whether the sequence converges or diverges. If it conve (-3)" 6n! an lim an

A:

Q: What are the first 5 terms of each defined sequence and give their associated series. Complete…

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Q: Is {-(n2)} n=1 to infinity, a convergent sequence in R with the usual metric?

A:

Q: Use only Definition 3.1.1 (or its negation) to prove the following: 2. Prove that the sequence…

A:

Q: Q1/ Isthe sequence {a,} converge ? († - ) -

A: If a sequence converges to some limit, then it is convergent; otherwise it is divergent.

Q: determine whether the sequence converges or diverges.if it converged find its limit.…

A:

Q: If the sequence {|]} converges to L, then the sequence {-m}converges to -L. Select one: O a. False O…

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Q: The sequence {5}-15: is: n=1 Converges to 5 Converges to Diverges. Converges to 10

A: Solve the following

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: Write the first 7 terms of the Fibonacci type sequence begging with 5,3. State as an exact radical…

A:

Q: Vn+I-yn 205. n

A: we have to test whether the given series is convergent or divergent

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: The first four terms of the sequence defined by An = nan-1+n'an-2, ao = 3, aj= 5 are ao = 3, a1 = 5,…

A:

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

A: Cauchy sequence and it's convergence

Q: If the sequence { 2 9 - An An - 3 converges to 6, then the sequence {an} converges to 9.

A:

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: Does the sequences converges or diverges ? ) , (Vm), (n²e-")

A: As per our guidelines we are supposed to answer only first three subparts of the question. Kindly…

Q: If the sequence { 2-4 an an+2 } converges to 7, then the sequence {an} converges to 9. True or…

A:

Q: 8. Determine whether the sequence an n3n converges or diverges. %3D

A: