For which series monotone and bounded sequences theorem can be opplied for the convergency 2" a, (n+2)! II) nt a, 1.3.5. (2n-D(2n +1) III) a 2.4.6 (2nX2n +2) O a all of them Ob ILI Oc none of them Od. LI O el

Q: One of the following sequences is divergent 2n en n=1 {(-1)• {, n2 +1 n=1 00 3n 1 (-1)ª. n2 + 7S n=2…

A: Second option is correct.

Q: One of the following sequences is divergent

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Q: True or false: The sequence True False {FL √√n=1 converges.

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Q: Let an = n> 1. In(2" +1)' 1. Determine if the sequence {an}n=1 is convergent or divergent. 2.…

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Q: By writing the summation of the three power series E nCx" +EC„x"-2+ £G,"-, we obtaln: O None of them…

A: Here we will 1st convert every series in such manner that every one will have same power of x in…

Q: all the sum symbols  ∑ go from 1 to infinity. Determine whether each of the following series are…

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Q: sin vn 2n Determine the convergence of the sequence an . If it converges, find lim an. BIU A E EV…

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Q: A sequence {a„}o is given by ao = v2, an+1 = v/2+ an. Find lim an. (Hint: lim an = lim an+1) пH00…

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Q: an= (-5)n an an = COS 4n+n3 3n+4" os(T) 8

A: The detailed solution with explanation is presented as the next step.

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: The. negation of (an) convergent is: a. Va, 3V, VN,3n > N: an € V b. 3a, VV,3N, Vn 2 N: an € V c.…

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Q: = 2√3 and bo = 3, and define two sequences recursively by √an.bn-1. Prove that {an} is monotonically…

A: let {an)Sequence  is monotonically decreasing if an+1-an≥0 And monotonically increasing if…

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: TRUE OR FALSE: (a) If Zan & E Can tbn) are both convergent, n=1 then Eon is convergent. hン1 C6) Yan}…

A: To do: State whether the given statements are true or false.

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: Are the following sequences convergent or divergent? If convergent, find their limit (a) an = √√n+1…

A: Solution: 4) a) Let  an =n+1-n                                        =n+1-nn+1+nn+1+n…

Q: Which of the following sequence is divergent? en {"} (-1)*+1 n s n² In+1 } {-3}

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Q: The multiplicity of -2 of the function P(x) = - x (- x - 2)?(x + 2) is: Select one: а. 2 b. 3 C. 4…

A: Note: you posted multiple question. As per our guidelines we are supposed to solve only one at a…

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

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

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Q: Q8 Let a, be the rth term of the series and the sum is defined by, n n(n + 1)(n + 2)(n + 3) ar 8.…

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Q: Let (x,) be a convergent sequence of real numbers and let (a,) and (b,) be subsequences of (x,) with…

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Q: Determine whether the following sequences converge or diverge. Answer "Converges" or "Diverges." nh…

A: Explanation of the answer is as follows

Q: Find a formula for the n th term of the sequence an whose first five terms are 0, 2, 6, 12, 20?

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Q: (a) Find a convergent subsequence of the sequence (an) defind by an = (-1)" + 5n 3n+1

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Q: Q1-A) Test the following sequence whether it is converging or diverging:- 2n 2. = [0.25m 2 ) ]…

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Q: Σ N 3 | n² 3 2 (n + 1)²

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Q: The sequence (Xn) = (1, 3, 1, 3, 1, . . . , 1, 3, ...) is: Converge to 3. O Divergent. Converge to 0…

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