What is the difference between the rate of convergence and the order of convergence? Have they any relationship to each other? Could two sequences have the same rate of convergence but different orders of convergence, or vice versa?

Q: true or false: if the sequence [a sub(n)] is monotone decreasing, then [a sub(n)] must converge

A: Follow next step

Q: Question 2.7. Show that the following sequence is : convergent. (ii). a₁ = = 0.1, a2 = 0.12,...,a10…

A: The objective of the question is to prove that the given sequence is convergent. A sequence is said…

Q: May I ask for a handwritten and non-AI-generated answer to this question since I really need a…

A: To prove that if a sequence {an​} is eventually monotonic, then it is either convergent, divergent…

Q: A sequer its Seco than its

A: We want to find the given statement is true or false.

Q: The greatest lower bound for the sequence {0.1,0.01,0.001, 0.0001, ...} is

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Q: is convergent to

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Q: Q1/ Is the sequence {a,} converge ? an

A: We have to find that given sequence is convergent or not . Find the limit of the sequence at n tends…

Q: a bounded sequence that is not convergent. (b) A sequence that is unbounded but it does not tend to…

A: We have to find out example of sequence with the given conditions.

Q: A sequence that does not have any convergent subsequence

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

Q: Can you further share how to find a convergent sequence

A: Given sequence  by  Here we consider two subsequences .Noted that A sequence  is convergent   are…

Q: Q1: Which of the sequences converge, and which diverge? n2 an 1-бп 1. 2. an 1+ 2n = [1+ 3n 3. an 4.…

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Q: 2n²+L 7 =

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Q: n-5 n+2

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Q: 3 Show that full range series is an extension of Half Rage.

A: we prove this statement using Fourier series. The Fourier series of half range even function or…

Q: all subsequences of a sequence converge, then the sequence itself converges. true or false

A: Topic:- algebra

Q: Determine if the sequence  {8/1 , 8/3 , 4/2 , 4/4 , 8/5 , 8/7 , 4/6 , 4/8 , . . .}  converges and,…

A: Given, Sequence S=81,83,42,44,85,87,46,48,...