4. (a) If (Cn)1 is the sequence Cn := ntn-2, compute lim,,0 Cn, sup{cn :n E N}, n2 and inf{cn : n e N}. Justify your answers.

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

A: Given to find limn→∞-n2+1-n2+n+2n

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim Sn = .…

A: Limit of a sn

Q: Write the first five terms of the sequence: +oo (11 ln n n n=1 Determine whether the sequence…

A:

Q: 9. Find the limit (if it exists) of the sequence (x_n) where x_n= n-3n^2.

A: Given xn=n-3n2

Q: True of False: If the geometric sequence {cr"}n2o (c # 0,r 0) converges, then the associated…

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Q: Find the limit of the sequence whose terms are given by: a-sub-n = (n^2)(1 - cos(6/n))

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Q: (n²)(1 - cos(뉴)). 1.5 COS An

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Q: Find the limit of next. sequence using the theorem for Limits 2n+1

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Q: Suppose that the sequence {n} is such that xn 20 for all n eN and that lim(-1)"xn exists. Show that…

A: We will use Triangle inequality.

Q: Compute the DFT for the sequence [1,1,1,1] x(0)= x(1)= x(2)= x(3)=

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Q: ä) {(3N +1)))(LI1)] (211)) 10. Prove that the sequence {(-1)"} does not converge.

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Q: A sequence is defined by tn = tn-1 +2", and t1 = 1. Determine the fourth term in this sequence.

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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: because 01. > 1. 1. en n-00

A: If x>1 then limn→∞xn does not exists.

Q: determine DFT for the sequence x(n) = [1,2,3,1]

A: Given: A sequence xn=1, 2, 3, 1. To find: Discrete Fourier transform of given sequence.

Q: Define the sequence{xn}by (see photo). Prove, using the epsilon −N definition, that this sequence…

A:

Q: Define the sequence {Sn} by Sn= [ 1 / (2)(1) ] + [ 1 / (3)(2) ] +   .............  + [ 1 / (n+1)(n)…

A: The nth term of the partial sum is given by

Q: Find the sum from k=1 to infinity of: [5/(3k+1)] using the limit comparison test.

A: Limit comparison Test:

Q: Find x so that x, x + 2, and x + 3 are consecutive terms of ageometric sequence.

A: We have to find the value of x such that x, x+2, and x+3 are consecutive terms of a geometric…

Q: Find the limit (as n → ∞) of the sequence an = In(2n² + 5) – In(5n² + 2), n > 1. %3D

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Q: Determine whether the sequence converges or diverges. 4n7t an = tan 3 + 16n lim an = DNE - 00

A: A sequence is called convergent if there is a real number that is the limit of the sequence. ... A…

Q: Find the limit of the sequence: 5n2 + 6n + 7 an 8n2 + 9n + 8

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Q: Find the limit of the sequence an={sin(n)/n}..if it exists.

A: Take limit n tends to infinity for finding the limit.

Q: Find the limit of the sequence: 2n2 + 1n + 9 An 4n2 + 3n + 6

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Q: 3.2.6 Theorem If X (x) then a < lim(x) b. is a convergent sequence and if a S X5bfor all n e N,

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Q: Suppose that {a, } and {b,} are two positive sequences, and define up . u /2n² + bn %3D If lim (a,)…

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Q: Additional Problem 2: Prove that the quantity tz =1+ ++...+!- In(k) is a monotone decreasing…

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Q: Find the limit inferior and limit superior of the sequence {[5 sin n]}.

A: The given problem is to find the limit inferior and the limit superior for the given sequence of {[5…

Q: A sequence is defined by tn=tn−1+3n and t1=1 Determine the fourth term in this sequence

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Q: 13. If x1 := 2 and x+1 = 2+1/x, for n 2 1, show that (x,) is a contractive sequence. What is its…

A: Given x1 = 2 xn+1 = 2 + (1/xn) We need to show that (xn) is a contractive sequence and we need to…

Q: Find the limit of the sequence whose terms are given by 5 (n²) (1 – cos an

A:

Q: For the sequence, determine if the divergence test applies and either state that lim n→∞ an does not…

A:

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim S, = 2…

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Q: 3] Prove that the sequence (x,) = (-1)"+' does not converge to any real number.

A:

Q: 5. Find the limit of the sequence 3. an ), n = 1,2, 3, --. 3JT

A: Explained below

Q: 2. Use the definition to prove that if (xn) is a sequence of real numbers which converges to -3,…

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Q: For the sequence, determine if the divergence test applies and either state that lim n→∞ an does…

A:

Q: 5. Show that the infinite sequence a, = Vn2 + 1 – yn² – 1 (n 1) converges by showing that it is…

A: Given sequence is  an= √(n^2+1) - √(n^2-1)

Q: Find the limit of the 4 n + 2 sequence lim . Show your work. V2 n+4 n- 00

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: For the sequence {a„}, with lim a, does not exist, this means the sequence diverges. Select one:…

A: 1. Let {an}∞n=0={(-1)n}∞n=0 is an oscillating sequence and for this:an=-1; n is odd1; n is…

Q: 2- Suppose that (xn) is a sequence such that xn > 0 for all NE N. 1 lim n 0 Xn Show that; Xn → 0 as…

A: I have proved using Apsilon delta definition

Q: Find a sequence X, such that it does not converge to any real number, but Y, does converge to some…

A: Consider the sequence Xn=(-1)n. Then Xn={-1,1,-1,1,-1,1,-1,1,...}. So, Xn does not converges to any…

Q: 1+ 2n² Xn {Tn} 1– 3n2 - Prove that the sequence where is bounded.

A:

Q: Write the first five terms of the sequence: 11 ln n) +oo Determine whether the sequence converges,…

A: To write the first five terms of the sequence.11 ln nnn=1+∞To determine whether the sequence…

Q: Find the limit of the sequence using L'Hôpital's Rule. 1(Vn² + 11 – Cn = n - n (Use symbolic…

A:

Q: The sequence fn is given as fı = 1, f2 = 3, fn+2= fn+ fn+1 for n > 1. How many even terms are…

A: The sequence fn is defined as follows, f1=1, f2=3 and fn+2=fn+fn+1 for n≥1 Find how many terms are…

Q: 5) Consider the infinite sequence defined as follows: B1 = 4 and, for each integer n> 1, B, = 3(…

A:

Q: For the sequence, determine if the divergence test applies and either state that lim n→∞ an does not…

A: