Vhich of the followings are false? is a decreasing sequence. 2" n 1 is not a bounded sequence. (nl) (2n)! V. I. is a divergent sequence. is an alternating sequence. O a. II, II b. I, IV O d. II, IV O e1, II, IV

Q: Evaluate the limit of the sequence or state that it does not exist. an = (2n + 5n + 1)/(5n)

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Q: - Provide an example of a sequence with the given propert a) a sequence that has subsequences that…

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

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Q: A sequence is said to be decreasing sequence if...... Vn>1 =S b O n+ 1 n n+1C O S 2n.d O n+1

A: Correct option :-  C Detailed Explanation

Q: A. Evaluate the following Infinite Geometric Sequences. 1. n-1 (8 n=1 2. (4 n=0 3. (8 n-1 n=1 ~ 3.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: +00 The sequence{Inc is n=1 (i) Converge (ii) Diverge

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Q: Consider the following sequence: {an} = {n – n² }, +00 Use an+1 – an to show that the given sequence…

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Q: A sequence is said to be decreasing sequence if Vn >1 2n.a O n+1 'n²³n+1·bO n+ n+1dO n+ 1

A: Given a statement

Q: Determine if the sequence is monotonic and if it is bounded. n! 4) 5n A) nondecreasing; unbounded C)…

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Q: 3 5 Consider the sequences, Which of these statements is correct? 2 5 8 11 A. The sequence converges…

A: Analysing this sequence we write the general term of the sequence as:                        an =…

Q: Which of the followings are false? I. 2 is a decreasing sequence. n²-1 I. is not a bounded sequence.…

A: A sequence u_n is decreasing if u_(n+1) <u_n for all natural number.

Q: 1. For the following sequences: Find if the sequence is arithmetic, geometric, or neither. Find the…

A: A detailed solution is given below.

Q: 27.The first and 25th term of the sequence an = (-1)"-1(n – 1) are both positive. Ο Α. True О в.…

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Q: (d) A Cauchy sequence with an unbounded subsequence. (e) An unbounded seuqence with a Cauchy…

A: The given problem is related with Cauchy sequence. We have to give an example of a sequence with the…

Q: 4. If a1 = 2 and az = 3 and an = an-1 + 3an-2 for n> 2, a. find the first five terms of the…

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Q: Which of the followings are true? 1. is a decreasing sequence. n²–1 is not a bounded sequence. I.…

A: A sequence bn is decreasing if bn+1≤bn for positive integers values of n. A sequence an is bounded…

Q: or each of the sequences described below, indicate which of the following properties describes the…

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Q: 4) Consider the following sequence: 1,5, 9, 13, 17,** a) Find a rule an for the sequence.

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Q: Determine whether the following statement is True or False: Suppose we have a sequence of natural…

A: Let the given sequence is  n1>n2 > n3> ...... Where n1 is finite and n1, n2, n3 ...are…

Q: 8. a) List the first five terms of the sequence defined by a, =7 3n-2 b) Determine whether the…

A: Since, you have post the multiple part's. I am answering the first three sub-part's. Please post the…

Q: 3. Express the following sequence in the form {a,} Term of Sequence 3,5,7.. Formula Notation a, =…

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

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Q: Choose the letter of the correct answer. If X is bounded sequence in R then X is convergent. a. True…

A: I am going to solve the problem by using some simple algebra to get the required result of the given…

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: (5) Give an example for each of the following statements, if it is not possible, explain why? (a) A…

A: Let's find.

Q: Which of the followings are true? * is a decreasing sequence. n²-1 I. is not a bounded sequence.…

A: Given below the detailed solution

Q: A sequence is said to be an increasing sequence if n+1 n+1 Sn2Sn+1 c O n+1

A: I will use the definition of increasing sequence.

Q: 2 Give examples of sequences, one in each case, of the following. (a) (an) is unbounded and not…

A: Since you have asked multiple questions, we will solve one question for you. For other question,…

Q: One of the following sequences is diverg 8. 3n (-1)" 1)" n2 +7 n=2 {8}n=1

A: Answer for this question is second option.

Q: Find a fomula for an given the few terms of the sequence. 1/2 , 1/4 , 1/8 , 1/16 , ....

A: We can solve the problem by obtaining the nth term of the sequence.

Q: Suppose c0, c1, c2, ... is a sequence defined as follows:  c0 = 2, c1 = 2, c2 = 6, ck = 3ck-3 for…

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Q: Which of the followings are false? is a decreasing sequence. 1. 2" n2-1 II. is not a bounded…

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Q: 3" 1 Determine whether this sequence is monotonic, and whether it is bounded above and below: a, =…

A: Consider the sequence an with an=3nn+1!. Replace n by n+1 in an=3nn+1! and obtain an+1=3n+1n+1+1!.…

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

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Q: 2. Find the limit of the sequence a1 = V2v2, as ai = V2, a2 = 2/2/2, 221 %3D a4 =

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Q: (d) Consider the sequence {an} C Q given by п 3 2,4, 7, 17 n+1 2n otherwise Prove the sequence is…

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

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

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Q: 3 Which of the following properties describe the sequence n3 Jn=4 Bounded, not monotonic Not bounded…

A: We have to choose the correct option according to the given options using the property of sequence

Q: 38 This sequence is non-linear 1, 2, 4, 8, 16, .. true O false

A: We will find the sequence is non linear in the following step

Q: Which of the followings are false? I. is a decreasing sequence. n² –1 I. is not a bounded sequence.…

A:

Q: 1. A sequence is defined by the recursive rule c, =c, 2" with c, =5. Which of the following…

A: Given a sequence:    cn=cn-1.2n-1          and c1=5

Q: Write the precise definition of the following: A sequence {Sn converges A sequence { Sn} is bounded

A: We will write the definition of sequence  converges and bounded

Q: 2. Which is (are) the initial condition(s) for the Fibonacci sequence? Fo=1, F₁ = 1 Fo=1 F₁ = 0…

A: We can solve this as follows:

Q: 10. Is there a pair of integers (a, b) such that a, x1, Y1,b is part of an arithmetic sequences and…

A: We have to find out that is there a pair of integers a,b.

Q: 9. Which of the following sequences is convergent? (A) (n). O (B) ((-1)"). O (C) (inn) O(D) None of…

A: Third option is the true one. See the step 2

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: 9. Which of the following sequences is convergent? (A) (n). O (B) ((-1)"). O (C) (sinn). (D) None of…

A: convergent sequence is(c)  sinnn

Q: Det ermine if the following sequences converge or O {3n2 -17 Lion +5n². diverge.

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.