Use Theorem 1 to determine the limit of the sequence or type DIV if the sequence diverges. an 49n2 45

Q: Give an example of a bounded sequence {a„}_1 having exactly 2 limitpoints.

A: we have to find a sequence such that it has two limit points.

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

A: Given that, an=21n2

Q: Find the limit of the sequence using L'Hôpital's Rule. b, = BVñ in(1 + 4) lim b in 123 Tutorial II

A:

Q: Determine the limit of the sequence or show that the sequence diverges by using the appropriate…

A: Given:   To find: The limit of C n  if it exist or to show the sequence diverges by appropriate…

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

A:

Q: Does the sequence {an} converge or diverge? Find the limit if the sequence is convergent. 4"

A:

Q: lim nsin(2/n) 2→+∞

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

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

A:

Q: 22: Establish the divergence of the sequence x, =(-1)"

A:

Q: Determine the limit of the sequence a, u UIS 3 Ve Divergent 4 1 5

A:

Q: Assume that the recursively defined sequence converges and find its limit. 10a a, = 10, an+1 (Type…

A: Use limit concept

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

A:

Q: Prove the sequence converges and find its limit.

A:

Q: Let {bn} be a sequence whose limit is 3. Show that if B is an upper bound of this sequence, then 3 <…

A: We will use the definition of limit.

Q: Determine the limit of the sequence or show that the sequence diverges by using the appropriate…

A: The sequence is defined by cn = ln8n-713n+4 To evaluate : limn→∞cn

Q: Exercise 4. Use the definition of limit to prove that the sequence {n – - is divergent. -

A: To prove: the sequence n-1nn=1∞ is divergent. limn→∞n-1n=limn→∞n-limn→∞1n…

Q: Determine the limit of the sequence or show that the sequence diverges by using the appropriate…

A:

Q: Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence.…

A:

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

A: we have to check sequence is convergent or divergent.

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

A: Give an example of a bounded sequence that has a limit.

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: consider the sequence  1, 1/2 ,1, 1/3 ,1 ,1/4, 1,.........  determine the limit superior and limit…

A: Given sequence 1, 1/2 , 1 , 1/3.. The limit superior is 1. As every number of sequence &lt; 1+k for…

Q: 1 lim n→∞ n² 0 =

A:

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

A:

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: Use the appropriate limit laws and theorems to determine the limit of the sequence or show that it…

A:

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

A: Given sequences (a) an=n-5nn (b) an=1+1n-n

Q: Evaluate this limit of sequence

A: The limit of a sequence can be found as  limn→∞an that is how the sequence behave when n tends to…

Q: Show that the converse of Theorem Limit of a Sequence is not true.

A: The theorem of Limit of a Sequence states that, " The function f be a function of a real number…

Q: use Theorem 1 to determine the limit of the sequence or state that the sequence diverges.an = 12

A: To use theorem 1 to determine the limit of the sequence.

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

A: Give an example of nondecreasing sequence without limit.

Q: (-1)" 50. Сп

A: To show that cn=(-1)n/√n diverges

Q: Find the limit of the sequence or determine that the sequence diverges

A: we have to solve

Q: Suppose (xn) is Cauchy and (yn) is bounded and monotone. Can we say anything about whether the…

A:

Q: Let (a,) be an unbounded sequence and (b„) be a convergent sequence. Prove that the sequence (a,-b,)…

A: In this question, we use the method of contradiction to prove the desired result.

Q: use the appropriate limit laws and theorems to determine the limit of the sequence orshow that it…

A: The given sequence is,

Q: Exercise 2. Use the definition of limit to prove that both of the sequences {+} and {"} converges to…

A: NOTE: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Show that the limit of a convergent sequence in a metric space is unique

A:

Q: a) an en 3n

A:

Q: Use the Theorem of Sequence Defined by a Function to determine the limit of the sequence or state…

A:

Q: use the appropriate limit laws and theorems to determine the limit of the sequence orshow that it…

A: To determine the limit of the sequence.

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

A:

Q: What theorem sometimes enables us to use l’Hôpital’s Rule to calculate the limit of a sequence? Give…

A: The theorem which enables us to use L'Hospital’s Rule  is,

Q: Determine if the sequence (nsin(pi/n)) is convergent or divergent. Find its limit if it is…

A:

Q: Determine if the following sequence converges or diverges. If it converges, compute its limit; if it…

A:

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

A: Since you have posted multiple questions. As per guidelines we will solve only first question. If…

Q: Use Theorem 1 to determine the limit of the sequence or type DIV if the sequence diverges. 7n An…

A: To find:

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…