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

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SUMMARY

The sequence \( \cos(n \pi) \) diverges as \( n \) approaches infinity. This is established by recognizing that the sequence oscillates between -1 and 1, creating two distinct subsequences: one converging to -1 and the other to 1. The unique limit condition for convergence is violated, confirming the divergence of the sequence.

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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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