Examine the increasing and decreasing of each of the following sequences, whether they are bounded or not. Thus, specify the characters (convergent or divergent) of the sequences. 1)(an)=(2n-1/1+3n)     2) (an)=(-1n/n)

Q: Let {an}=1 be a convergent sequence such that a1 = V5 and an+1 = V5 a,n. Compute lim an.

A: The sequence an is convergenta1=5 and an+1=5 an

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 a divergent sequence {an} such that {a2n} converges

A: Let us take: {an}= {-1, 1, -1, 1, -1, 1, -1, .......} This is an alternating series. So it diverges.…

Q: Every bounded sequence is convergent. True False O

A: A sequence is of the form an The limit of the sequence is obtained as limn→∞an=L Bounded sequence: A…

Q: Prove that the sequence {cn} converges to c if and only if the sequence {cn- c} converges to 0.

A: To prove that the relation between the limits of the two given sequences

Q: Determine whether the sequence converges or diverges. an = (1 + 2j• п

A: To check whether sequence is convergent and divergent.

Q: Every bounded sequence has a convergent subsequence. True O False

A:

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

A: Given sequence is, an=n3n3+1

Q: Let {an}n=1 be a convergent sequence such that a1 = v5 and an+1= /5an Compute lim an n→∞

A: Given a1 = 5  and  an+1 = 5an

Q: Suppose that the sequence {n} is such that xn 20 for all n eN and that lim(-1)"xn exists. Show that…

A: We will use Triangle inequality.

Q: If the sequence {a}, is convergent, then the sequence {x} defined by a₁+as+as++an-stan is also…

A:

Q: If the following sequence converges, find its limit. If the sequence diverges 7−n4

A: The given sequence is not convergent.

Q: The sequence a, is converges to 0 a divergent sequence попе converges to 8

A:

Q: If sequences {an} and {b} both diverges to infinity, then the sequence an {a}} bn is convergent.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Every pointwise convergent sequence is uniformly convergent sequence. ylgn İhi O

A: Solution  True Statement  Detailed Explanation :-

Q: 3. Determine if the sequence xn = 47² is convergent or not and find its limit if it exists n²+1

A: We want to find the given sequence is convergent or divergent.

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

A:

Q: ) Examine the increasing and decreasing of each of the following sequences, not. Thus, specify the…

A:

Q: Examine the increasing and decreasing of each of the following sequences, whether they are bounded…

A: (i) The given sequence is an=n+11+3n To find: the given series is increasing or not, bounded or not,…

Q: 3n The two convergent subsequences of the sequence (-1)+2 is

A: xn=(-1)3n+2 x2n=(-1)3(2n)+2=(-1)6n+2x2n-1=((-1)3)2n-1+2=(-1)2n-1+2    as (-1)3=-1

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

A: Given, an=n-1n!

Q: Determine whether the sequence {2n+3 / 5n−7} converges or diverges.

A:

Q: Every convergent sequence is bounded. O True O False

A: Every convergent sequence is a bounded sequence, that is the set {xn : n ∈ N} is bounded. Remark :…

Q: 6n Determine if the sequence an 4(-1) converges or diverges. If it converges, compute its limit. If…

A:

Q: Determine whether the sequence converges or diverges 1+(-1)" а. An n2 b. an =(1 -3zn) 3n.

A: For the solution of the problem follow the next steps.

Q: Determine the convergence or divergence of the following sequence. If the sequence converges, find…

A:

Q: Is the sequence divergent or convergent? {vn - vn+1}

A: n  - n+1 =(n  - n+1) (n  +n+1 )/(n  + n+1) n  - n+1  = (n - n - 1)/(n  + n+1)  n  - n+1  =  - 1/(n…

Q: + 3n –n

A:

Q: Let ₁1 and In+1 = limit. 1 for n N. Show that this sequence is convergent and find its In + 2

A:

Q: 1. Prove that the sequence converges to . 2n+1

A:

Q: Prove that a bounded decreasing sequence {xn} converges by using the e− N definition of convergence…

A:

Q: – 2n2 1+n² 2n²

A: Sequence is convergent.

Q: Give an example of each of the following, or indicate that no such example example exists by writing…

A: An example for a convergent sequence that is not bounded. Let A=an be a convergent sequence. Then ,…

Q: Prove that the limit of the convergent sequence is unique.

A:

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

A:

Q: prove that the sequence (1/5^n) is convergent and approaches zero?

A: Series and sequences

Q: (b) Examine the increasing and decreasing of each of the following sequences, whether they are…

A:

Q: Determine whether each sequence converges or diverges; if it conv In(n +a) lim where a and b are…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each…

A: an=ln2n+1n Now, limn→∞an=limn→∞ln2n+1n=limn→∞12n+1·21       By using L'Hospital's…

Q: If possible, give an example of 2 convergent sequences an and bn such that E(an + bn) diverges.

A:

Q: 1.) Determine whether the sequence converges and if it does then find its limit: (п-1)! an = n tan…

A:

Q: For the sequence {a„}, with lim a, does not exist, this means the sequence diverges. Select one:…

A: 1. Let {an}∞n=0={(-1)n}∞n=0 is an oscillating sequence and for this:an=-1; n is odd1; n is…

Q: Examine the increasing and decreasing of each of the following sequences, whether they are bounded…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2n + 1 n=1

A: We have to check sequence convergence.

Q: Supply a proof for Theorem 2.6.2.(Every convergent sequence is a Cauchy sequence.)

A: Solution: Consider the given statement is "Every convergent sequence is a Cauchy sequence" Let xn be…

Q: 1. Determine whether the sequence converges or diverges. If it converges, find the limit. 2n an 3n+1

A: Use limit ratio test to simplify and solve the problem easily.

Q: an = 0 and bn Σ-1 bp Show that if lim n converges then En-1an converges too.

A: Given that:            limn→∞anbn=0 and ∑n=1∞bn converges. Prove ∑n=1∞an converges.

Q: Determine if this sequence converges og diverges: n3/(cos n+ 5n)

A: We have to solve given problem: Concept:

Q: An 1+- n

A:

Q: The sequence a = is a divergent sequence o converges to 8 none O converges to 0

A: Given: an=8nn For sequence, an, if limn→∞an+1an>1, then sequence is divergent.

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.