In 3n an = In 5n

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

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Q: Determine if the sequence bn =  (2n2)/ln(n+5) is convergent or divergent. If converges, find the…

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

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

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Q: Find the sum of the convergent series. 1.6

A: Gp

Q: Find the sum of the convergent series. 3+.

A: We need to evaluate the sum of the following convergent series 3+32+34+38+···········

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

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Q: In(4n) In(3n²)

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Q: determine the limit of the sequence or show that the sequence diverges. an = 10n/n!

A: A sequence is convergent if the limit for the sequence exists as n approaches infinity, if no limit…

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

A: We find the limit of the an th term. limx→∞(an)=limx→∞1+(-1)nn=1+limx→∞(-1)nn=1+0=1

Q: 2. Give an example of an unbounded sequence {an} of negative terms such that an does not diverge to…

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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: Cn = Jns -Jn? 13 ニ

A: The given sequence is an=n3-n2.

Q: Determine if the sequence converges or diverges: In n n2

A: To check whether a sequence is convergent or divergent first calculate its limit if limit is finite…

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

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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: State if the sequence {xn}1 define below is convergent or divergent: fix -1< a < 1, and let xn =…

A: The convergence of the series can be checked by applying the limits to ∞. The convergence of the…

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

A: Given: a. an=n2e-n, b. an=-1nn2+1n2+3

Q: Every bounded and monotonic sequence is divergent. Select one: O True O False

A: We know that monotonic increasing                 (or decreasing) sequence which is bounded above…

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

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Q: 11. b) Determine whether the sequence an = 2- cos(n) is convergent or divergent.

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Q: The sequence{In©}, is ) Converge (ii) Diverge

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

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Q: Doesthe series * 2n Converge or diverge フー一 30-2

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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: 00 Ink

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

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Q: Determine whether the sequence converges 1) а, 3D п sin

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Q: Inn en n=1

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Q: Find the sum of the convergent series.

A: The given series is a geometric series with common ratio less than one. So we can use formula for…

Q: Show that the sequence ffn}, where fnox) = ne is uniformly convergent nx+1 on [a, b], aso but is…

A: Given: fnx=nxnx+1 To show that the given sequence is uniformly convergent on a,b, a&gt;0

Q: a1 1 an+1 = 4 – an for n 2 1 %3D

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Q: Show that (1/n²+ n+1)!nEN is a Cauchy sequence.

A: Solution :-    The given sequence is              an =   1/( n2 + n + 1 )     ;  n belong to N .…

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: Determine whether the sequence converges or diverges an = In(n + 1) – In(n) %3D lim an %3D n- 00

A: Given sequence is an=lnn+1−lnn We have to find the limn→∞an Use property lnm−lnn=lnmn…

Q: Find the sum of the convergent series. Σ

A: The given convergent series is, ∑n=0∞-47n To find its sum.

Q: Determine whether the sequence converges or diverges. If it converges, find the limit. In(5n)…

A: Find the limit of the sequence, in order check the sequence converges or diverges.

Q: { n2 100 3n+6 Jn=1

A: Explanation of the answer is as follows

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

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Q: Determine whether the sequence 5n is convergent 3n2 + 2n +1

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

A: We have to solve given problem: Concept:

Q: Define a recursive sequence by a1 = 2 and an+1 = 1 − a2n. Either prove that (an) converges or prove…

A: Define a recursive sequence by a1 = 12 and an+1 = 1 − an2. Check the second term: a2 = 1 −122=34 It…

Q: 3+5n 1. an n+n

A: the given sequence,an=3+5n2n+n2

Q: determine whether the sequence {√ n+2 - √ n+1} is convergent or divergent

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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: 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: 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.