QUESTION 14 14. Which of the following sequences is/are convergent? (-) n I. an = 4n2 II. an n² + 3 2n III. an = n2 (A) I only (В) II only (С) III only (D) I and II only (E) II and III only О (4) О (В) (E)

Q: 1 The sequence converges to - 2 /n² – 1 – /n² + n 20 Select one: True O False

A: The sequence 1n2-1-n2+n   converges to -2    we have to check it is true or false.

Q: What is the sum of the infinite series 4 2n 37 ()* 37 2 2 1 +...+ (-1)" + (2n+1)! •• ? 3! 5! 7! O -1…

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Q: Find the n" term a, of a sequence whose first four terms are given. 9 10 11 -- -- 4' 8' 12' 16

A: Given:-84,-98,-1012,-1116,....

Q: Which of the followings are false? I. 0 (-1)" is absolutely convergent. Ln=1 n² +Inn 2n II. E (-1)…

A: we have to check each options

Q: 7. Let {an1 and {bn}1 be convergent sequences with limit A and 0, respectively. If bn 0 for all n N…

A:

Q: Which of the following statements is /are not true? I: Every convergent sequence is Cauchy. II:…

A: A sequence is called a Cauchy sequence if the terms of the sequence eventually all become…

Q: 84x n Define the sequence {bn} by b₁ Show that the sequence {bn} con- Let {an} be the sequence…

A:

Q: %3. 8. Em-1

A: the given series is divergent,

Q: Let (a,) be a sequence converging to 1 with a, 21 for all n. Which of the following conditions…

A: Given a sequence converging to 1

Q: convergent serie 12) Find the sum of each 2 A) / + = + ( ² ) ² + ( ² ) ³ + ( ²1 ) 4 + ... ( - )^² +…

A: Let's find sum of given series.

Q: 58. Which of the following sequences is/are not convergent? I: a, := n+1 3n2-4 ,n 2 1 II: a, := n+1…

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Q: 1 1 1 1 Ex. 1. (a) If an 1.2 2.3 3.4 п(п + 1) then show that {an} is a bounded monotonic increasing…

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Q: The Cauchy condensation test The Cauchy condensation test says: Let {a,} be a nonincreasing sequence…

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Q: 1. Determine whether the following sequence converges or diverges. If the sequence converges, find…

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Q: Sequences and Series Arithmetic and Geometric Sequences and progressions. 1. Write down the first…

A: nth term given , We have to calculate first 5 terms for each :

Q: Assume that the sequence converges and find its limit. 72 a, = 4, an +1- 1+ an for n = 1, 2, 3, . O…

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

Q: 8 2. If the series 4 5 16 32 +... converges, find its sum. Otherwise, say it diverges. 25 125 (A)…

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Q: 2. (a) Write the first 5 terms of the sequences with general terms an below and indicate whether…

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Q: (1) List the first 5 terms of oach of the soquence (a,). n+1 (d) an = sin An = 3n- - 1 3(-1)" (e) a…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Give e-N proof to show that the sequence {1} converges to 1 as n →∞.

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Q: Let {A,} be a non decreasing sequence of events of S, then lim P(A,) = P (lim A,) = P| U An %3D n =1

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Q: Consider sequences (– 1)"n (i) Зп — 1 (1) cos T- (ii) n2+ 3n (iii) Зп2+ 5 n Which of the following…

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Q: 6. Which one of the following statements is true for the convergent sequence (a )? (A) Every…

A: In general every convergent sequence is Cauchy. But in  complete metric space both convergent and…

Q: 3. Discuss the convergence or divergence of E=1(2"e"). 4. If (an) is a bounded decreasing sequence…

A: As per guideline we have to solve one question

Q: Which of the followings are true? 1. E (-1)" is absolutely convergent. m-D1 n+inn II. En-1 2" (-1)8r…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: n2 - 1 8. 5. {2" + n}n-2 A 6. n + 1 n-3 (-1)" (-1)"-1 n² 7. an 8. an 4" 10. a, = 1 + (-1)" 9. a,=…

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Q: Which one of the following sequences does diverge to infinity? Oa. an Inn O b. an In 2n OC. 2n O d.…

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Q: Which of the followings are true? (-1)" is absolutely conuo

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Q: Which step of the following of the proof of the fact that "if a -→ a, as n 0o, then JaJal" not true?…

A: For 1st the B option is correct .

Q: 2n 18. а, 1+ %3D n

A: Note: