3n The two convergent subsequences of the sequence (-1)+2 is

Q: A decreasing sequence where cn is greater than or equal to 1 for all n. If this sequence could…

A: A decreasing sequence where cn is greater than or equal to 1 for all n. That is, cn≥1, the sequence…

Q: (a) The nth term of a sequence is Un. The sequen

A: Introduction: 1: the sequence in which things are or should be linked, related, or dated Follow the…

Q: a1 =-1, an+1= An +6 An +2

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Q: Find the limit of the sequence, or show why it doesn't exist, an = n4-(n8-n5)1/2.

A: Given,  Sequence                     an = n4-(n8-n5)1/2

Q: Determine if the following sequence converges or diverges. an = -10(n!) (-8) Note: If it converges,…

A: Given: an=-10n !-8nTo check: Whether the sequence converges or diverges.

Q: Find the conditions necessary for this sequence to be Cauchy. Хп xn+1 = axn+b 1 + xn

A: For the sequence (Xn)(Xn​) defined by the recurrence relation to be Cauchy, the condition necessary…

Q: 1 2n+3 - whether an C. Is the sequence bounded? is increasing, decreasing or not

A: a sequence {a_n} is called bounded if there exists two real numbers m and n such that…

Q: Find the first 10 terms of the sequence an Its 9th term is Its 10th term is 1 an-1 and a₁ = 18.

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Q: Determine whether the sequence {2n+3 / 5n−7} converges or diverges.

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Q: determine whether the sequence is monotonic,whether it is bounded, and whether it converges. an =…

A: Given the sequence an=2n-13n. To determine whether the given sequence is monotonic, whether it is…

Q: A sequence that does not have any convergent subsequence

A: We find a sequence that does not have any convergent subsequence.

Q: 2n Using the definition of a convergent sequence, prove lim n-00 3n+1 3

A: Suppose limn→∞2n3n+1=13 then for a given ε>0 , there exist a natural number  N=N(ε)  such that…

Q: ∞ If the radius of convergence of the series Σ unx" is R then the radius of n=1 of the series un x²n…

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Q: In 3n an = In 5n

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Q: 1 Decide whether the sequence an converges and if so, calculate limno An : 3n - 2n 4n an

A: To decide whether the sequence  converges and if so, to calculate .

Q: ii. an 5n²+4 n²+2

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Q: For each sequence below, explain why the sequence diverges or find the value that it converges to:…

A: Given sequence: n-2e3nn10+6en The main objective is to explain why the sequence diverges or find the…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.