In which of the following options, the statements given below and the general terms an that satisfy these statements are matched correctly? I: E is divergent when an is convergent an n=1 n=1 II : is divergent when an is divergent an n=1 n=1 III: T: is convergent when the sequence {an}- is divergent

Q: 3. n-3n+5 n7 Sn=1

A:

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: Given a sequence (u): Which one of the following statements is true? A If (u) is bounded then it…

A:

Q: 2. Let 0 b, for each n e N. With the fact in part (a), by simple computations (you should try it as…

A:

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

A:

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

A:

Q: Which one of the following statements is CORRECT? O A. Every bounded above monotone sequence…

A: A is correct. For false I have given counter example

Q: Evaluate the following and determine if the sequence {a,} converges or diverges 20n2 5n +1 - an %3D…

A: Given,

Q: (a) If (an) is a sequence such that (an bn) converges to zero for every sequence (bn) converging to…

A:

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

A:

Q: Which of the following is true about the sequence In (3n -n²+1) - ln(n³ + 2n¹ +5n)? = an 3 The…

A:

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

A: here we use p series test given by : The series 1/n^p convergence if p>1 and diverges if p<=1

Q: Which of the following is true about the sequence In (3n² − n² + 1) − ln(n³ + 2n¹ + 5n)? = an The…

A:

Q: Consider the following sequence: 9" {an} %3D 4n2 n=1 An+1 to show that the given sequence {an} is…

A: This question is related to sequence and series, we will solve it using given information.

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 statements is false? O A. The sequences {a,} and {bn} must be positive for…

A: Solve the following

Q: Let (an), (bn) be sequences, so that (b,) is defined as b, = an – an+1· Prove that the series b, n=1…

A:

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,…

A:

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

A:

Q: 2. Which one of the following statementa is not true for the convergent of the sequenceat & (A)Every…

A: There are given some statements

Q: Show that E-2 ((In n)ª/n²) converges for -o 1. n=2

A:

Q: Consider the sequence In(1/n) An V2n first five terms of an , and find lim„→c∞ An - If the sequence…

A: Here we have ,  an=ln1/n2n Here we have to find first five terms,

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

A:

Q: Which of the following statements is true? a. The sequence {e"}, is bounded, monotonic and…

A: Check each of the following sequences is bounded, monotone, divergent and converges sequence.

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

A: I-M II-L III-K

Q: Suppose that a, > 0 for all n and that an diverges. Suppose that b, is an arbitrary sequence of…

A: We have to solve this question with the help of comparison test:

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>1 and diverges for p≤1. 1) ∑an is…

Q: IN. 13. Consider the following sequence: a. Determine whether the sequence {an} is monotonic. If so,…

A:

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: Define a sequence (an) recursively by setting a1 = V2 and an+1 = v2+ an for n > 1. (a) Show that an…

A:

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: 00 00 Show that > n3 + 8n converges by using the Direct Comparison Test with En3. n=1 n=1

A:

Q: Which of the following sequences is strictly decreasing None 1 {-1)",! n+ 2 S n=1 n+ 3 n=1 00 1 n+3…

A:

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

A: Calculus   sequence

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

A: Consider the given information: Here to match the statements and given general term an. Here option…

Q: 1. Consider the sequence {an}, where a, e [a, b] for all n e N. Show that is convergent.

A:

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

A:

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

A: P-test : Consider series ∑an=∑1np P-series converges only if p&gt;1 and diverges for p≤1. 1) Given…

Q: Write the Örst 5 terms of the sequences with general terms an below and indicate whether they are…

A: We need to write the firrst 5 terms of the sequences with general terms an below and check whether…

Q: (a) If {an}=1 and {b„}n=1are both sequences of real numbers where 0 < an < bn and En=1 bn diverges,…

A:

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: Given a positive sequence {a,}n>o satisfying Vai > yao + 1 ana a < 1 An+1 an-1 for any positive…

A:

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

A: We consider each of the cases L,M,N and match them with I , II, and III

Q: If the sequence (s_n) converges, then so does every subsequence of (s_n). True False

A: Suppose s_n be a convergent sequence. We have to check the statement that every subsequence of s_n…

Q: Let {an} be a positive monotonic sequence with sup an = 12345. Which of the following statements is…

A: Counter example: For option E:  {an}=12345/n for all n€Natural no.  This is positive monotonic and…

Q: 6. Which one of the following statements is true for the convergent sequence (a )? 5(A) Every…

A: Sequence and it's convergence

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.