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

In summary, we discussed the convergence or divergence of the sequence {cos npi} with n to infinity. Using the fact that if a sequence converges, the limit is unique, and that all subsequences converge towards the same limit, we can see that this sequence converges towards two different numbers, -1 and +1. We also briefly touched on the concept of a subsequence and the importance of understanding limits in analysis.
  • #1
teng125
416
0
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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  • #2
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?
 
  • #3
is it -1 and +1 ??
 
  • #4
Is there a doubt in your mind?
 
  • #5
yaya.pls explain to me
 
  • #6
Is this in the context of an analysis class?

Are you familiar with the two theorems I quoted in my first post?
 
  • #7
no,what is subsequence??
 
  • #8
First answer my question, teng:
What is meant by a "limit"?
 
  • #9
I put this conversation in your hands arildno, I have to leave. :smile:
 

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

1. What does "cos n pi" represent in this question?

In this question, "cos n pi" represents the cosine function with an input of n multiplied by pi. This means that the angle being evaluated is changing as n increases.

2. How does n to infinity affect the convergence or divergence of this expression?

As n approaches infinity, the angle being evaluated in the cosine function also increases. This means that the output of the function will oscillate between -1 and 1, leading to divergence.

3. What is the difference between convergence and divergence in this context?

In this context, convergence refers to the output of the expression approaching a specific value as n increases. Divergence, on the other hand, refers to the output oscillating or approaching infinity as n increases.

4. Can you provide an example of a similar expression that converges?

An example of a similar expression that converges would be "cos n", where n represents any real number. In this case, the angle being evaluated remains constant, leading to a constant output of the cosine function.

5. How does the value of n affect the convergence or divergence of this expression?

The value of n plays a crucial role in determining the convergence or divergence of this expression. As n increases, the angle being evaluated in the cosine function also increases, leading to divergence. However, for smaller values of n, the expression may converge to a specific value.

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