In which of the following options, the statements given below and the general terms an that satisfy these statements are matched correctly? 1 is divergent when > an n=1 I: an is convergent n=1 II: > is divergent when > an n=1 an is divergent n=1 is convergent when the sequence {an}- is divergent an n=1 III: 1 K: an =n М: an - n L: an 2 (а) I-М (b) I-L (с) 1-М (d) I-L (е) 1-К II - K II-M II -L II - K II - M III-L III -K III - K III- M III - L

Q: If an converges and > 0 for all n , can anything be said about E–? An an

A: Given that, ∑ an  converges We known that, the series if  ∑n = 1∞ an  is convergent then limn→∞ an =…

Q: One of the following sequences is divergent 2n en n=1 {(-1)• {, n2 +1 n=1 00 3n 1 (-1)ª. n2 + 7S n=2…

A: Second option is correct.

Q: Which of the options is correct for the following sequence- {n(-1)* Sn=0 ütfen birini seçin:…

A: Here, the given sequence is: n(-1)n+2n=0∞ So, the terms of the sequence are: a1=1(-1)1+2=-1

Q: One of the following sequences is divergent None 00 2n2 + 1 1 (-1)" 2+ 3n2 n=1 00 3n ) (-1)". n² + 7…

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Q: In(n+1) n-2 is divergent. The sequence an %3D Select one: True False

A:

Q: Which of the following assertions is true for the given sequences? a) {(-1)" e"} converges п+1 b)…

A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :…

Q: 4.W: Which of the sequences {an} converge and which diverge: 1-n 3 n+(-1)" 2. an 1. an 70- 4n2

A: Convergence and divergence of the sequence

Q: 1 The sequence converges to - 2 n² – 1 - Vn2 +n Select one: O True O False

A:

Q: Which one of the following statements are NOT correct? I. If E an is conditionally convergent, then…

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Q: One of the following sequences is divergent 2n en n=1 2n +11 -1)" 2+3n2 n=1 O None 8. 3n -1)" n2 + 7…

A: Two options are divergent in the above questions; 2nd and 4th options are divergent. Find the…

Q: Let a, be a sequence of real numbers such that an+1 2 an, Vn 21 and a, + a as n + o. Use this…

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

Q: One of the following sequences is divergent S 2n l Ten In=1 3n ° 1)" n² +7. n=2 O None n- -1)" n² +…

A:

Q: Which of the following inequalities can be used to show that +1 n=1 converges? 1 O n3 +1 nº + 1 O n°…

A: The series ∑n=1∞nn3+1. We have to find which of the following inequality can be used to show the…

Q: One of the following sequences is divergent O {8}1 n=1 3n (-1)". n2 +7 n=2 S 2n len n=1 O None 2n2…

A: LET'S FIND, DIVERGENT SERIES .

Q: {«,} Given the sequences such that -2<a <5, then which of the following statements is true? O A. By…

A: The given question is related with sequence. Given a sequence an such that -2 &lt; an ≤ 5 . We have…

Q: Which of the following sequences is strictly decreasing 00 In+2 n=1 n+2 J n=1 n + 1 O None

A: Decreasing sequence.

Q: Q22. A Sequence has been defined as the following 7an a1 = 1, An+1 2+ an You must find its limit,…

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Q: 1. Determine whether the following sequences converge or diverge. If the sequence diverges, state…

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Q: 3. Prove the statement: If the series > an is convergent, then a, →0 as n→ 0. Is it also true that…

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Q: One of the following sequences is divergent 2n2 +1 (-1)" 2+ 3n2 n=1 {8}n=1 O None 8. 3n {(-1). n2 +…

A: As we know that;   For divergent limn→∞an≠0 or limit does not exist.   Now check; a)…

Q: 1 79. For which a does converge? n(In n)" n=2

A: Let the given series be - y = ∑n=2∞ 1nlnnuWe can write it as - y = ∫2∞ 1nlnnadn…

Q: 29. Which of these statements is/are true? I. A sequence a, in R converges to a* if and only if…

A:

Q: In which of the following options, the statements given below and the general terms an that satisfy…

A: P-series test:  ∑an=∑1np  P-series is convergent for p&gt;1 and diverges for p≤1. 1) ∑an is…

Q: One of the following sequences is divergent 3n (-1)n. -1)". n2 + 7 n=2 2n2 +11° (-1)ª 2+ 3n2 n=1 2n…

A:

Q: Which one of these sequences is convergent Select one: O a. none of these. Ob. 2n+9 n' nt О с. 2n+6…

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Q: 1. Suppose {an} and {bn} are positive sequences and that there exists N so that n >N = an < bn. Show…

A: We use the Cauchy criterion to prove the result.

Q: 10. Suppose {an} is a sequence of real numbers and b, the sequence {bn} is convergent, so is {an}. =…

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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: In which of the following options, the statements given below and the general terms an that satisfy…

A: The divergence test states that if limn→∞an≠0 then the series ∑an will diverge. A sequence an is…

Q: If 2 an converges for some large k, then so will ) n=k n=1 Select one: O True 17 O False

A: It can be solved using the simple observation.

Q: Given the sequences (a) such that - 2<a55, then which of the following statements is true? O A. By…

A:

Q: 7: Which of the following statements are always true? (i) E (-1y"e!/n converges. n=1 (ii) The…

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Q: 1.5 Show that the series (a – 6)(a – 26) „3 + (a- b)(a- 26)(a- 35) | z+- 2! 3! 4! converges…

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Q: Use the difference an+1 - an to show that the given sequence {an} is strictly increasing or strictly…

A: given sequence n7n-6n=1∞

Q: Consider the following sequence: {a,) = {n – n²} Sn=1 Use an+1 - An to show that the given sequence…

A: Calculus   sequence

Q: One of the following sequences is divergent 3n (-1)" n2 + 7 n=2 n2 (-1) n2 +1 n=1 2n n=1 O None…

A: The infinite sum is said to be divergence when n→∞, the summation limn→∞an≠0 and limn→∞an does not…

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

A:

Q: Which of the following statements is (are) true? If an has a finite sum, then lim an = 0. 818 n=1 ∞…

A: To connect connect option from given question.

Q: A sequence {an} is said to converge to a real number L if for every e > 0 there exists a positive…

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Q: 01: Which of the sequences converge, and which dive 1-6n 2. an an =(1+ 3n %3D an = 1+ 2n ملف

A:

Q: 9. If the series ) 3 converges, then A k> -1 B k>0 C k> 2 D k> 3

A: We need to find all the possible values of k for which the given series converges.

Q: In which of the following options, the statements given below and the gener terms an that satisfy…

A: We know that ∑1np is convergent for p&gt;1 and divergent for p≤1   Consider K: an = n2{an} =…

Q: 3. Prove each of the following. (a) If a converges, then Ei, must diverge. 1+ ak (b) If an 20 for…

A: Idea: If series is convergent then its corresponding sequence is converges to 0. Other ideas we are…

Q: Use the difference anti-an to show that the given sequence {a} is strictly increasing or strictly…

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Q: If (x,) and (yn) are two sequences in R, such that x, < yn Vn E N and lim,c. Yn = ∞, ther lim,-o Xn…

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Q: Determine if the two given converges or diverges. { п n 2n + - 1/ n=1 Σ n n \2n + 1 n=1

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Q: In which of the following options, the statements given below and the general terms an that satisfy…

A: proof :  Taking k : an = n2              ∑n=1∞an=∑n=1∞1n2 limn→∞1n2=1∞2 (taking limit)=1∞=0  Thus,…

Q: write down detailed e− N-proofs  i) (√n+7)/(n+5) converges.  ii) (n2−3i)/(2n3+2i) converges

A: Follow the steps.

Q: True or False? You do not need to prove your answers. a) A sequence (an) converges to L if and only…

A: We will prove it

Q: One of the following sequences is divergent 3n (-1)n n2 + 7 n=2 3. n=1 (-1)* n=1 O None

A:

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.