Test for converge: 8 n=1 (2n-1)!! 2n!! 2 . Note n!! (n!)!. n!! is the product of all positive numbers up to n that have the same parity as n (odd or even)

Q: (a) Develop an estimated regression equation for these data. (Round your numerical values to two…

A: Give value: Xi Yi 6 5 11 9 15 13 18 19 20 30 So, the equation of line is:…

Q: Prove that if the sequence {an} is divergent and the sequence {bn} is convergent, then the sequence…

A: Given: The objective is to prove that if the sequence {an} is divergent and the seqence {bn} is…

Q: Does it converge: ∑(sqrt(n+1) - sqrt(n))/sqrt(n2+n) if so what is the sum (show steps please)

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Q: a_k=a_(k−1)+4k + 1, Vk ≥ 1, k € Z, a_0=0 Find explicit formula for a n use iteration, sum of…

A: Given ak=ak-1+4k+1,forall k>=1 k∈Z,a0=0 To find an explicit formula for an, we will use iteration…

Q: Find the limit of the series 3-1 + 3-2 + 3-3 + ...+ 3-n+ ... additionally, write the sum in sigma…

A: Given: series is 3-1+3-2+3-3+…+3-n+… To be find: limit of the series and write sum in sigma…

Q: Which of the following sequences is a convergent and decreasing sequence with least upper bound 1?…

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Q: Does it converge: ∑(sqrt(n+1) - sqrt(n))/sqrt(n2+n) if so what is the sum (show steps please)

A: We apply limiting comparison test to calculate

Q: an n In n en (domain n ≥ 1)

A: Given that an=nln(n)en We have to find it's limit when n tends to infinity.

Q: 1S niformly ) Let {n} be a sequence of real numbers and x E R. Suppose there exists M = N such that…

A: To prove that the sequence {xn​} converges to x, we need to show that for any given ϵ>0, there…

Q: O True False is a sequence of real numbers and The monotone convergence theorem states that a…

A: We use various results from real analysis

Q: 1. Prove that the sequence {4+} converges to 4.

A: To know weather two function converge or not take difference of them and put limit to infinite. If…

Q: 2. Let an be the sequence given by An = 2n 0 if n is a power of 22 otherwise What is the radius of…

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Q: AN A integer diverges {an} for any K to 2, Σ on SEQUENCE GIVE EXAMPLE OF where an Converges 3…

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Q: SELECT (n!)? (2n)! .()* B) is similar to G A) converges C) is similar to )" D) diverges

A: We will use Ratio Test to determine convergency

Q: 3 9 9 27 81 20'40'80' 160

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Q: Prove that each of the following sequences diverges: (a) {4n - 5} (b) {√3n+ 1} 2n + 3 √n n² +7 8n +3…

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Q: Study the sequence below using Cauchy sequences. V₁ = Cus (a) + Cus (2a) +----+ Cus (na) 23 2.s with…

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Q: 4n5 Vn E N, let an 8n5 +1 (a) State whether the given sequence {a,}nEN is convergent or not. If it…

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Q: Give e-N proof to show that the sequence {1} converges to 1 as n →∞.

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Q: 4 4 Write the sum 4 3 + ... using summation notation with n as the index of summation. (Using…

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Q: Which of the following is a sequence that increases convergent and has a maximum lower bound of 1?…

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Q: The ratio test can be used to check if the series n! Σ n =1,n converge or diverge Select one: True…

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Q: a) 29,1+ 29, 2C1+ 1) (2+9) 4+9 (i) comment whe ther the sequence is converges ordiverges (i oblain…

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Q: n - 1 converges absolutely because lim - 2 (n – 1) R=1 True O False Reset Selection

A: Consider the given series.

Q: Use Cauchy Criterion to prove that the sequence {sn} converges where Sn + Sn-1 Sn+1 n > 1, 2 and…

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Q: Write the terms of the given sequence and then graph the sequence f(0) = 16 f(n) = 0.5f * (n - 1) ,…

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Q: Define A, = {a,r' : a, E R} for i = 0,1,2, , Construct an increasing sequence of sets that produces…

A: Given: Ai=aixi : ai∈ℝ for i=0, 1, 2, ⋯ To construct: An increasing sequence of sets that produces…