Let a, = (-1)" + -, vn 2 1. Which of the statements below is/are true? I: Ja,|S 2, Vn 2 1 II: lim,- sup a, = 1 and lim,-o inf a„ = -1 III: a, is a convergent sequence. A. I and II only B. I only C. II only D. I, II and II E. None of the above.

Q: Q1. From your registration number of the form SP20-BCS-013, create a sequence S in such a way that…

A: The registration number is: SP20-BCS-013

Q: 1. Write the first five terms of the sequence defined by i) a, = (-1)"+1 Li. ii) b, = . 2. Find a…

A: Given: Question 1(i)  an=(−1)n+11+nn!(ii)  bn=2nn!find five termsQuestion 2(i)…

Q: 25) Show that the sequence (2/7) n! 10") +∞ n=1 is eventually strictly decreasi

A: The given sequence is: {10nn!}n=1+∞ which is to be shown as decreasing. First, we shall know the…

Q: 30. а, 2 1+ %3D - n

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Q: The sums of nth term of three arithmetical progression are S,,S, and S,.The first term of each is…

A: We will solve the problem

Q: 10. (6 points) A sequence is given by the recursive definition an = an-1 + 2, ao = 3. a) Find a₁,…

A: The objective of the question is to find the first three terms of the sequence defined by the…

Q: 11. (6 points) A sequence is given by the recursive definition bn = 4bn-1, bo = 3. a) Find b₁,b₂,…

A: The objective of the question is to find the values of b_1, b_2, b_3 and a general formula for b_n,…

Q: (a) (². ¹) If the sequence (an) is defined by the recursive formula an+1 = -2-a, a₁ = 1, then (an)=1…

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

Q: The limit of the sequence a.- (1+ (a) - (3) e) (c)e None(e)

A: This is 1 to the power infinity form question so accoding to that I wrote the formula to Solve this…

Q: 6.0. 3) What are the first three terms of the sequence defined by the recursive formulas t₁ = 2 and…

A:

Q: 1. Write the first five terms of the sequence п а) а — 3" п b) а, = sin п c) a̟ = (- 1)'(÷) (–…

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Q: 3 an +2 A sequence of real numbers a, is defines inductively as a, = 1 and an+1 = n2 1. %3D an +3…

A:

Q: Q8) The sequence 5 +(-1)" an' a) converges to 1 b) converges to c) converges to 0 d) diverges |5

A: an = 5+(-1)n5      = ∑n=1∞5+(-1)n5 =∞ ∑n=1∞5+(-1)n5 diverges to ∞

Q: 3 a, +2 A sequence of real numbers a, is defines inductively as a1 = 1 and an+1 n 2 1. an+3 Use this…

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Q: 35 (b) (5+7k) = k=D1

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Q: (a,) be a Cauchy sequence of nonzero real numbers. Which of the following statements about (a,) may…

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Q: 5. If a = (1+ 1)", then which of the following statement is true for the nth term of the sequence…

A: The solution is given as follows :

Q: 8. Consider the sequence {an} such that an+1 = -3 – 2an. Then lim an = -1.

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Q: and (bn) be two sequences of real number disprove each of the following statements: n=1 n=1 ¹) If…

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Q: What are the first four terms of the sequence n+1 00 3n-1 n=1 Select one: 3 2 4 3 O None of the…

A: Given problem:-

Q: 10. Let {xn} be a sequence of real numbers. What does the limsup of this sequence mean?

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Q: ! 3) Determine eat for anthmeric sequence a = -15, 9, 82-85 SI-A PISK.C@ $10.011X

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Q: 1- 5: Express the following as sequence of the indicated terms: 1 Ea, +- 1. 2' 10 а, 'i+1 2. 3.

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

Q: 12. The sequence des First five terms of the sequence: Domain: Range: Maximum: Minimum: -10 -10 Y -5…

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Q: Which of the following sequences represents an arithmetic sequence with a common difference d = -3?…

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Q: Let (a,) and (bn) be sequences in R and define c, as follows: For each natural number n, let c, =…

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Q: 5. (a) Let {an} be a sequence of integers with 0 an10-" exists (and lies between 0 and 1). (This,…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1. Let a, = 1 and an+1 = 1+ 1+an (a) Find the first six terms of the sequence {an}. (b) Prove that…

A: As you asked multiple sub parts so I answered 1st three subpart.

Q: A sequence is said to be decreasing sequence if

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Q: = {1,2,...,100} then H is equal-- {1,2,3,...,1

A: We are entitled to solve one question at a time , please resubmit the other question if you wish to…

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.