Suppose you know that  {an} is a decreasing sequence andall its terms lie between the numbers 5 and 8. Explain whythe sequence has a limit. What can you say about the valueof the limit?

Q: -n +1 lim -n2 +n +2

A: Given to find limn→∞-n2+1-n2+n+2n

Q: I have to determine if this is an increasing or decreasing monotonic sequence. The steps need such…

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Q: EXAMPLE 8, Does the sequence whose nth term is n п + An n 1 - converge? If so, find lim,»oan.

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Q: Find S,, the sum of first 15 terms of the arithmetic sequence: , 0, – - 1, .... ...

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Q: Find the limit of the sequence with the given nth term. n + 5

A: Given sequence is an = (n+5)/n

Q: What is the 46th term in the arithmetic sequence –1.5, –1.3, –1.1, -0.9, .?

A: we have to find out the 46th term

Q: Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?

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Q: Find the limit of the sequence with the given nth term. n + 6 n

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Q: Whst is the exact value of the limit of the sequence (7^(n+1)-7)/7^n?

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Q: Explain why you think the sequence { n+1 converges to a finite number or diverges. If the sequence…

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Q: tim п-х 2 (n-3₂²)

A: Given;  limn-infinity (n-3n2).

Q: Explain: e is really the limit of a sequence, and the value usually stated, 2.71828… is a numerical…

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Q: The greatest lower bound for the sequence {2, 4, 8, 16, 32, 64, . } is

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Q: Consider the sequence {. n+2 1. Determine the number of terms that are not within ɛ = 0.0002 of 3.…

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Q: What is the 46th term in the arithmetic sequence –1.5, –1.3, –1.1, -0.9, ...?

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Q: What is the 8th term of the sequence whose ?th term is defined as ?? = (−1)^n(3n-2)

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Q: What does it mean for a sequence to be defined recursively?

A: A recursive sequence fnnadditionally known as a recurrence sequence is a sequence of numbers f(n)…

Q: 2. The missing term of the geometric sequence 45, [ ],1620, . is ...

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Q: What is the exact value of the limit of the sequence -n^3/(n^4+1)?

A: To determine the value of the limit.

Q: Find the infinite sum of the geometric sequence with 2 if it exists. 7 a = 4, r = -

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Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: Given that: The sequence an = 3n( n + 2) .

Q: me sequence whose nth term is

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Q: 3. Evaluate the limit of the sequence or state that it does not 2" + 5**1 exist. 5"

A: Limits exists and limit value is 5 .

Q: Find the sum of the finite geometric sequence whose first term is 1.2, whose ratio is 0.5, and which…

A: Topic:- sum of GP

Q: Determine the sum of the first 10 terms of the sequence whose general term is given by ((3^n) – 2).

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Q: consider the sequence  1, 1/2 ,1, 1/3 ,1 ,1/4, 1,.........  determine the limit superior and limit…

A: Given sequence 1, 1/2 , 1 , 1/3.. The limit superior is 1. As every number of sequence < 1+k for…

Q: Determine whether the sequence with  an = n*e-n for n = 1, 2, 3, . . . is increasing, decreasing,…

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Q: Give an example of a single sequence that meets all the following criteria, or explain why this is…

A: This is not possible.   Result : every bounded below and decreasing sequence of real numbers are…

Q: Explain why you think the sequence converges to a finite number or (n+1)! diverges. If the sequence…

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Q: It is a sequence where every term after the first is obtained by multiplying a non-zero constant. O…

A: To tell which is the sequence where every term after the first is obtained by multiplying a non-zero…

Q: Find the infinite sum of the geometric sequence with 2 if it exists. 8 6, г a = -

A: The geometric sequence with a=6, r=28

Q: Find the nth term of a sequence whose first several terms are given. 3, 5, 3, 5, 3, 5, . . . an

A: We have to find nth term

Q: Find the first four terms of the arithmetic sequence whose first term is 6 and whose common…

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Q: If {b,}-1 is a bounded sequence and lim,→∞ An = lim,-+∞ anbn? Justify. 0, what can you say about

A: Given that  bn is bounded sequence, so, by definition of bounded sequence  ∃B>0 such that bn<B…

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: The given sequence is an = (3/2)n A sequence an is monotonic when its terms are non-decreasing…

Q: Find the first four terms of the arithmetic sequence whose first term is 9 and whose common…

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Q: Find the nth term of a sequence whose first several terms are given. 3, 5, 3, 5, 3, 5, ... an =

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Q: Find the infinite sum of the geometric sequence with a =2 r=2/6 if it exist

A: The geometric sequence with a =2, common ratio r=2/6

Q: Find the sum of the finite geometric sequence whose first term is 1.6, whose ratio is 0.5, and which…

A: Gp

Q: Determine the limit of the sequence defined below. an 13 n+5 If the limit does not exist, enter Ø.…

A: limn→∞-113nnn+5 =limn→∞(-1)n113nnn+5 let n is even (-1)n=(-1)2m=1 L=limn→∞113nnn+5=0*1=0 let n is…

Q: A sequence is said to be decreasing sequence if

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Q: { Explain why you think the sequence converges to a finite number or diverges. If the (-8)"- ル-1…

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Q: Discuss the non decreasing and Bounded of the sequence 5,5,5,5,5

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Q: The term of an infinite sequence is 2n^2-n. Write the first six terms of the sequence and explain…

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Q: {an} = {} 4 2

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Q: consider the sequence 1,1,2,1,2,3,1,2,3,4,1,2,3,4,5,.... determine the limit superior and limit…

A: We have to find limit superior and limit inferior

Q: What is the connection between the concept of the limit of a sequence and the limit of the function?

A: Solution

Q: Find the nth term of a sequence whose first several terms are given. 7, 2, –3, –8, ... an

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Q: Use a graph of the sequence to decide whether the sequence is convergent or divergent. If the…

A: First we draw the graph of an  and if the graph converges to a number k then the sequence an…

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.