May i know (cos n pi ) with n to infinity is converges or diverges?

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Homework Help Overview

The discussion revolves around the convergence or divergence of the sequence defined by (cos nπ) as n approaches infinity. Participants are exploring the behavior of this sequence within the context of mathematical analysis.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the convergence of the sequence and discussing the uniqueness of limits. There is an inquiry into the existence of subsequences that converge to different values, with some suggesting potential limits of -1 and +1.

Discussion Status

The conversation is ongoing, with participants seeking clarification on concepts such as subsequences and limits. Some guidance has been offered regarding the properties of convergent sequences, but there is no explicit consensus on the convergence of the sequence itself.

Contextual Notes

There is a mention of the context being related to an analysis class, and some participants express unfamiliarity with key concepts, indicating a potential gap in foundational knowledge.

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may i know (cos n pi ) with n to infinity is converges or diverges??

may i know (cos n pi ) with n to infinity is converges or diverges??
 
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Use the fact that if a sequence converges, the limit is unique, and the fact that if a sequence converges towards x, all subsequences converge towards x also.

Can you find 2 subsequences of {cos npi} that converges towards different numbers?
 
is it -1 and +1 ??
 
Is there a doubt in your mind?
 
yaya.pls explain to me
 
Is this in the context of an analysis class?

Are you familiar with the two theorems I quoted in my first post?
 
no,what is subsequence??
 
First answer my question, teng:
What is meant by a "limit"?
 
I put this conversation in your hands arildno, I have to leave. :smile:
 

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