Answered: The limit of the sequence {an}{an}as…

Name: The limit of the sequence {an}{an}as nnapproaches infinity equals ll i
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Description: The limit of the sequence {an}{an}as nnapproaches infinity equals ll iff ∀ε>0 ∃ m ϵ N ∀?>0 ∃ ? ? ℕ s.t. whenever _______ , ________.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The limit of the sequence {an}{an}as nnapproaches infinity equals ll iff ∀ε>0 ∃ m ϵ N ∀?>0 ∃ ? ? ℕ s.t. whenever _______ , ________.

Expert Solution

Step 1

Given that,

The limit of the sequence {an} as n approaches infinity equals l.

Definition of the limit of a sequence:

We say that x is the limit of the sequence (x_n) if the following condition holds:

For each real number , there exists a natural number N such that, for every natural number , we have .

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