1 The sequence converges to ,? – 1 – V n² +n | Select one: True 21 False

Q: Q1/ is the sequence {a,) converge > sin n

A: We have to find given sequence is convergent or not .

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: Which of the sequences {a,} converge and which diverge: n+(-1)" 1. a=

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Q: Assume that the following sequence converges aj = 2, an+1=1+÷One of the following is true Select…

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Q: What is true for the sequence of general terma, =1+(-1)" ? Select one: O converges to 2 O None of…

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Q: The value ofk that makes the following sequence is converge to * : (7/6) as n approach to infinity…

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

A: Given,

Q: Q1 Which of the following sequences converge? In (n") (2n+1) an (n+4)! d, = be %3D %3D (n+1)! {a,),…

A: Which of the following sequences is convergent?an=2n+1!n+4!bn=πnn100cn=lnn10ndn=n4n+1!

Q: Consider the sequence defined by an = 1-- e-cn, n21. For what real number(s), c, does the sequence…

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Q: n+5 a. (xn) = п-5 n² b. (xn) = %3D п3+1

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

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Q: Which one of the following sequences converges? OA. OB (-1)" 7 5" oc (-1)" n 7n +2 n? OD (-1)". 5n +…

A: Disclaimer: "Since you have asked multiple questions, we will solve the first four question for you.…

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 following sequences converge or diverge. If the sequence converges, determine…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Q4) which of the sequence below converge, and which diverge? 1- 5n • Un n4+ 8n3 • U, - In (" *!)".…

A: Note: Our guidelines we are supposed to answer only first three subpart . Kindly repost other…

Q: (8) Determine whether the following statements are true and give an explanation or a counterexample.…

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Q: If a, converges and a, > 0 for every n, show that 4converges. What can you say about a for any…

A: Given: ∑n=1∞an converges and an>0 To prove: ∑n=1∞an2 converges. Proof: ∑n=1∞an2=∑n=1∞an2 Since…

Q: The sequence {5}"-1 is: is: 00 O Converges to 10 O Converges to Converges to 5 Diverges. H/5

A: The given sequence is: 5n=1∞

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

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Q: 2. Which of the following sequences converge to zero? n2 (a) n2 + 1 (b) 2" (c)

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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: 00 For which a does > n(In n)a converge? n=2

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Q: n! The sequence converges to 0 (100)6n Select one: O True O False

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Q: We say that a sequence of real numbers (xn)nɛN converges to the real number а, if Ve > 0,3N E N, Vn…

A: Given sequence is xn=-1n+2-n. Definition: A sequence of real numbers xnn∈N converges to the real…

Q: Find a closed form solution for the following recursive sequence: An = an-1+ 2" for n > 2 with the…

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Q: If (Xn) is a monotone sequence, then (x,) converges O False O True

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Q: 1 Q:: If En=1 find the following: - Vn+1+vn 1- The sum of sequence? 2- Determine, if the sequence…

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Q: 5. The sequence . is convergent in (R. d). a. True b. False

A: 5 -b(false)

Q: Prove that the sequence defined by a1 = −3 and an+1 = (1/4)(2an-1) converges. Then prove that it…

A: Given sequence is defined by a1=-3, and an+1=142an-1  ,n>1 We have to prove the sequence…

Q: The general term of the sequence is Select one: O True O False 1, an = 1-1 1 (-1)"+1 ,n21

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Q: 1. Determine if the following sequences are convergent or divergent. Show all steps. a) an = (-1)n…

A: SOLUTION-

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: 103n2 – 8 - 1. Xn := 4n2 + 99n + 3 1i. Xn := -n + Vn² + 3n 3n? + 2n iii. Xn := 2n n=1 8.

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Q: Which of the following sequence is divergent? en {"} (-1)*+1 n s n² In+1 } {-3}

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Q: The sequence 7² – 1 - V n² +n converges to – 2 Select one: 23 True O False

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Q: Does the sequence xn ={n=1 converge in (0,1) ? why ? 100 %D

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Q: 9. Find the explicit formula for a sequence satisfying а, %3D10а,, + 25а, _,n22 n-1 а, %3D 3, а,…

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Q: 4. Suppose (xn) converges, and let K be a positive integer. Now create a sequence (yn) by changing…

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Q: If the sequence {|]} converges to L, then the sequence {-m}converges to -L. Select one: O a. False O…

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Q: Which of the following sequences are convergent sequences? Select all that apply. 7" O an n7 1 O an…

A: sequences are given, we have to find the convergent sequence

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

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Q: The sequence (-1)n+1 In=1 converge to is (i) Converge (ii) Diverge

A: The given sequence (-1)n+1n=1∞

Q: the sequence converges or diverges. {an} = {: 5n5 + 8n³ – 12 } %3D n3 +3n2 -7n + 8

A:

Q: EX check the convergency of the following sequences (n+1)2

A: Convergence of the sequence

Q: (b) Show that the following sequence is convergent: 1+ (-1)" n² Yn = √2+ (c) Show that (yn)neN is…

A: A Sequence <an> is convergent if and only if limn→∞ an is finite and unique.

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…