Using only the Archimedean Property of R give a direct E-N verification of the convergence of the following sequence: {   [ 2 / (n^(1/2) ) ]  +   [ 1/n ]     +      3  }

Q: Find a divergent sequence {an} such that {a2n} converges

A: Let us take: {an}= {-1, 1, -1, 1, -1, 1, -1, .......} This is an alternating series. So it diverges.…

Q: [n^2cos(n/2)] / 2n^2 +1 does this sequence converge or diverge & w

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Q: Find convergence radius of sequence  Σ (x^n/n(n+2))

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Q: 33. Σ &"(x − 2)" n=12

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Q: {xn} is a bounded sequence such that all convergent subsequences converge to the same number

A: Every bounded sequence has convergent subsequence.

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: lim (1+1)". (a) Define the sequence {bn} by b₁ = 2, and for n ≥ 2, Recall that e lim bn = bn-1 +…

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Q: Can you further solve how exactly to find a convergent subsequence here?

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Q: find if it converges ∑∞ n=0((4n)!(1103+26390n))/(3964n (n!))  (show each step please)

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Q: Which of the sequences {a,} converge and which diverge: 1. a, = 2+ (0.1)" 2. а, 1+-

A: 1) an=2+0.1n We know that if -1<r<1 then limn→∞rn=0 So, limn→∞0.1n=0 Thus, limn→∞2+0.1n=2+0=2…

Q: Write out the first five terms of the sequence with, [(1 - 7)", determine whether the sequence…

A: To write out the first five terms of the sequence with 1-7n+7nn=1∞, to determine whether the…

Q: x = -1/n when n is odd, and an = 1/2" when n is even

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Q: Suppose that the sequence {an} is monotone and that it has a convergent subsequence. Show that {an}…

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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: Consider the sequence 1 Ik 2(1.9*) a) Find the values of r1, r2, r3, and r4, round to four decimal…

A: In the given question, the sequence is given as: xk=121.9k

Q: Q1:- (A) Discuss the convergence of the given sequence : a(n) = cosh ln(n) (B) Evaluate: f dxdy…

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Q: 17. (a) (b) Give an example of a convergent sequence (x) of positive numbers with lim(x+1/xn) = 1.…

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Q: Limit Type Tier Expression Notes Examples = n" = n! Convergence Two examples Super Large N/A among…

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Q: +00 2n determine the interval of convergence of (-1)"+1 n3 + 2 n=1

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Q: Is {-(n2)} n=1 to infinity, a convergent sequence in R with the usual metric?

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Q: (b) Why? ) Consider the sequence {an = (-1)"}n€Z+· Is it divergent or convergent?

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Q: 1. Prove the sequence {a,} = (1 +-)" Converges to the limit e*, what about the sequence {b,} = (1…

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Q: For the sequence {a_n}up ∞ down n=0 with limn→∞ a_n=0, this means the sequence diverges. T/F

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Q: D{(;;)"} [Select]

A: Note: Hi! Thank you for your question. As per the guideline we can solve one question at a time in…

Q: Determine whether each of the following Sequences is convergent. Justify!! @@ (x₁) where x := n 16.…

A: Determine whether each of the following sequences is convergent. Justify.C.   where .

Q: (-1)"n (xn) = п+2

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Q: ax Examine the convergence of , where a>1. x (log xy" +1

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Q: Verify that x = 1/a is a fixed point of the function g(x) x(2 ax). Determine the order of…

A: To show that x = a is a fixed point of g(x)=x( 2-a x) it is sufficient to show g(a)=aand if we can…

Q: prove that the sequence (1/5^n) is convergent and approaches zero?

A: Series and sequences