let (sn) be a convergent sequence, and suppose lim sn > a. Prove there exists a number N such that n > N implies sn >a.

Q: Suppose an is a sequence which converges to a real number L. Suppose also that K is a real number…

A: Given that sequence (an) converges to real number L.a If an ⩾ K for all n∈ ℕ then L, whether L⩾Kb If…

Q: These are alternative definitions of the limit of sequences. Can you please help identify what is…

A: Given: limn→∞an=a if ∀ε>0∃N∈ℕ such that ∀n≥N  an-a3<ε To Find: Identify what is wrong with the…

Q: 2. Suppose f : R" →R satisfies the following: whenever {r,} C R" is a sequence satisfying lim In =…

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Q: 3. Let (Sn) be a sequence of nonnegative real numbers, and suppose lim s, = 0. Prove that lim S, =…

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Q: If a sub 1=1 and a sub (n+1)=3 - 1/a sub n, what is the limit of a sub n as n approaches infinity

A: Limit

Q: how can i apprach this problem

A: The objective of this question is to find the limit of the sequence (n+1) as n approaches 0 using…

Q: 6) 1 n 1- cos

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3. Consider the definition of the limit of a sequence in calculus. We can say that the limit of a…

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Q: an + an-1 An+1 Vn +1 (a) Find the limit of an as n → ∞ and give a proof. converges for a,n from part…

A: Given, an+1=an+an-1n+1 the sequence is all positive number. (a) we need to find the limit of an as…

Q: A.) If {a,} is a convergent sequence, then {a,} is also a convergent sequence. B.) If f(x) is a…

A: This question is related to sequence and series.

Q: 12.M. Apply Example 12.3(d) and the preceding exercise to the sequence (n"/n!) to show that n lim…

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Q: . Find two sequences {an}o and {b»}_o such that lim 0o. As part of your solution, explain…

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Q: 2. (30 points) So far in the course, we have only talked about sequences which converge to some real…

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Q: 1. Use the definition of the limit of a sequence to establish the following limits (a) <-0. +

A: Given, a limit of a sequence: It is required to prove the above limit using the definition of…

Q: Determine whether an = limit if it converges. In (5n+2) In (2n-3) converges or diverges and…

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Q: (b) lim(n+1-n)=0.

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Q: (e) lim Vn2 +2 -n = 0

A: Limit of the indeterminate from

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.