If the terms of one sequence appearin another sequence in their given order, we call the first sequencea subsequence of the second. Prove that if two subsequencesof a sequence {an} have different limits L1 ≠ L2, then 5an6diverges.

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

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Q: Use any method to prove that if X = (xn) is a Cauchy sequence of real numbers, then () is also a…

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Q: Determine the limit of the sequence a, (-1)* 1 1 2 2 - 1 Divergent

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Q: let a,=!. Consider the sequence dany generaed as follows: = It I Itan a ntl (a) Write down expresian…

A: We will answer the first two questions since we don't answer multiple questions at a time. Please…

Q: The limit of the sequence a, = (-1)"2 is equal to %3D Select one: True O False

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Q: The limit of the sequence z = Arg(-i+) is equal to

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Q: use Theorem 1 to determine the limit of the sequence or state that the sequence diverges. bn = 5n −…

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Q: Prove that a sequence in ℝ can have at most one limit

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Q: For the sequence {an}o with lim an exists, this means the sequence converges. Select one: O True O…

A: First is true and second is false.

Q: Find the limit of the sequence an = In(9n +7) – In n. If the limit does not exist, type "Diverges"…

A: Solution:

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

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Q: Suppose that ho, hị, h2, . is a sequence defined as follows: ho = 1, h1 = 2, h2 = 3, %3D hy =…

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Q: If ( a n) is a sequence that diverges to ∞, prove that Iim n --> ∞ (1/a n) = 0

A: Assume that the sequence an diverges to ∞. That implies, limn→∞an=∞.

Q: determine whether the sequence is monotonicand whether it is bounded. an = (3n + 1)/(n + 1)

A: To check the given sequence is monotonic: Consider Take derivative; We see that the first…

Q: Assume that the recursively defined sequence converges and find its limit. a1 = - 2, an +1 = /14 +…

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Q: the Sequence hver So Lalue. for

A: The given sequence is,

Q: En3D1 In(n) 2 +1

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Q: In a metric space (S, d) every convergent sequence is a Cauchy sequence. Is the statement True or…

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

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Q: If (an) is a sequence converging to L, prove that (an)=1 converges to L.

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Q: Find the generating function of the sequence {a;}k20 defined by ak = -3 if k even; a = 3 if k odd.…

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Q: Find the limit (as n → ∞) of the sequence an = In(2n² + 5) – In(5n² + 2), n > 1. %3D

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Q: Find the limit of the sequence {an} if 1 - (1)/(n) < an < 1 + (1)/(n), forevery integer n ≥ 1.

A: Given: 1-1n<an<1+1n where n≥1 We have to find the limit of the sequence an:

Q: Please help

A: The given recursively defined sequence is

Q: Suppose that a sequence is defined a=-3, + 10 n-1 List the first four tor mc of th

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Q: Find the limit of the sequence an= 3n−4/2n+3

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Q: Find the limit of the sequence or determine that the limit does not exist. n! an= 4n.7n

A: Consider the given sequence, an=n!4n·7n

Q: Suppose that {a, } and {b,} are two positive sequences, and define up . u /2n² + bn %3D If lim (a,)…

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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: If (xn) is a Cuachy sequence in R, then .it is unbounded :Select one True False

A: We Know that A sequence {n}is called a Cauchy sequence if for any given ϵ > 0, there exists N ∈ N…

Q: 2n+1 if n is odd if n is even an

A: Find the limsup and liminf

Q: Consider the sequence  1,1/2,1,1/3,1,1/4,1, ... Determine the limit superior and limit inferior of…

A: Given sequence is  1,12,1,13,1,14,1,....... By observation , it can be seen clearly that 1 repeats…

Q: 2. Suppose x,, X2 , X3 ..... Isa sequence defined by x, = 2, X2 = 4, bk-2 + 2bk-1 for all integers k…

A: Since you have asked multiple questions, we will solve the first question for you. Note:- In…

Q: 82n 46. аn n!

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Q: Find the limit of the sequence {an}, or show that it diverges: An 2n +1 In

A: Topic - limits

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

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

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Q: Please give an cxample of a sequence (a,) such that: (a) (an) is not bounded above. (b) (an) is not…

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Q: Find a closed formula for the sequence with recursive : 2 = 1 and a2 definition an 2an An – 2 with…

A: Given  an=2an-1-an-2  , a1=1 , a2=2 we have to find the closed formula for this sequence.

Q: Let an be the nth term of the sequence 1,2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,…

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

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Q: Please solve...

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Q: If the sequence {a,} is defined as follows: Ha,=1, a,+1= 15-a, for n > 1 then as %3D %3D

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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: Determine if the sequence  {8/1 , 8/3 , 4/2 , 4/4 , 8/5 , 8/7 , 4/6 , 4/8 , . . .}  converges and,…

A: Given, Sequence S=81,83,42,44,85,87,46,48,...

Q: Consider the sequence {x} defined by n n+1 +In(1/n²) ifnis odd Is the sequence divergent or…

A: Since answering more than one question is not in our scope, rest can be reposted.

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

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

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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.