Finding Limit of Sequence: Determine if Exists & Find Solution

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Homework Help Overview

The discussion revolves around determining the limit of the sequence defined by a(n) = cos[n/(2^n)]. Participants are exploring whether the sequence has a limit and how to find it, particularly as n approaches infinity.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the approach to finding the limit, with one suggesting the use of L'Hôpital's rule. Others are clarifying the context of the limit, specifically whether it is as n approaches infinity.

Discussion Status

The discussion is ongoing, with some participants providing insights about the behavior of n/(2^n) as n tends to infinity and its implications for the continuity of the cosine function. There is no explicit consensus on the method to be used, but there are productive lines of reasoning being explored.

Contextual Notes

There is a lack of explicit information in the original problem statement regarding the limit's context, leading to assumptions about n approaching infinity.

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Homework Statement



Determine whether the following sequence has a limit. Find the limit if it exists.

Homework Equations



a(n)=cos[n/(2^n)]



The Attempt at a Solution



Im not sure how to go about finding the limit...do i use l'hospital's rule?
 
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When talking about limits you usually specify limit as n approaches something, do you mean infinity?
 


It doesn't actually say in the question, so i am assuming it means as n tends to infinity.
 


It should be obvious that n/2^n goes to 0 as n goes to infinity. Then use the fact that cos(x) is a continuous function.
 

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