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: .4 || (cos²e + sin?e) dp dz de 8 2(0*cos?8 + p*sin?e) p dp dz de

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Q: D prove tHhat kin

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

Q: Solve for the value of "b" in the equation: * (12) + b 11 Your answer

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Q: Let (a,) be a sequence converging to 1 with a, 21 for all n. Which of the following conditions…

A: Given a sequence converging to 1

Q: Compute the sum 2* Sum(n=2 to 8) (1/2) n-7

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Q: Does the sequences increasing or decreasing ? (1-) , , (n – 2"), (n – n²) п ;) , (n – 2") , (n – n²)…

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Q: This is a sequence, which test should I use and is it convergent/divergent? Explain. {(-1)n (n+1),…

A: This is a sequence which test should I use and is it convergent/Divergent? {(-1)n(n+1)!/3n!}…

Q: strong induction ICt

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Q: Q9) Find the rule for the nth term (term an )of the following sequence: a) 2, 6, 18, 54, ... b)…

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

Q: whether the statement is true or false. a) Sequence is convergent if and only if monotone.

A: False

Q: True or false: if (n) converges, then every subsequence (n) is Cauchy. Select one: O True O False

A: True or false

Q: Determine whether the sequence is monotonic. Prove you are correct. (a) {} 2n (b) n (-1)* ) (c) n2…

A: a and b are monotone but c is not

Q: Vn2 + 1 Let (bn)neN be the sequence defined by b, 2n Let e > 0. Derive a value of N (in terms of e)…

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Q: What is the formula for the following summation? n=1 c(n) Option 1 Option 2 n(n+1) n(n+1)(2n+ 1) 21…

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Q: Every bounded sequence converges. True or False?

A: False

Q: 3+6 n i) The sequence ) is bounded by 4 n <ns ii) The 8 th. element of this sequence is

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Q: an n In n en (domain n ≥ 1)

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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: Determine if the sequence is monotoric and if it is bounded. fo 7. an = (n+7) ! (n+1)!

A: A sequence {an} is monotonic iff an&gt;=an+1 or an&lt;=an+1 for all natural number n. A sequence…

Q: Q\ Is the sequence (Vn + 11 – vn+1)y bounded ? nEN Neither Yes No

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Q: Let F, F₁, F2, ... denote the Fibonacci sequence. Find an expression for (Fk+ 1)² – (FK)² a…

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Q: Bonus. Suppose that {a,}n is a convergent sequence and that {b„}n is a divergent sequence. Can the…

A: {an+bn} can't be convergent.

Q: 2. Prove the sequence an = n"/n!, n > 1, is %3D (a) increasing; (b) not bounded above (show an 2 n).

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Q: Q3/ Find out the convolution of two sequences given below: X(n) = x1(n) * x2(n) X1(n) = { 1, 0 , -3…

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Q: Only use epsilon defination , Let be a sequence of positive terms such that pn-> p show that…

A: We apply only Epsilone defination.

Q: 3" n=1

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Q: Given the sequence 41, 4.4 what is f(n)? 4+ f(n)=4+ f(n)=n+ f(n)-5-- 4+n 1 4+n n

A: We rae required to find the general term of the given sequence.

Q: 7n+2 lim no 8n + 100 = NIN

A: