Understand the Difference Between Convergence and Divergence of x(n)

  • Thread starter fireflies
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In summary, the conversation is discussing the differences between two questions in a math assignment and the solutions to these questions. The values of x in the table are different, but the question is why the solutions are also different if the questions are the same. The other person suggests that the solutions may start with different x values and have additional steps that lead to the same final answer.
  • #1
fireflies
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I actually don't know what math sub-topic it belong to..

To the question, I got this two in my class assignment. Why x(n) is different can anybody tell me? What is the difference in these two questions (except that the one has 10 included and other not. Is the difference for that?)??
 

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  • #2
The values of x in the table are different.
 
  • #3
yes, but that's the solution. My question is there is no difference in question, so why in solutions?
 
  • #4
Usually when they say "Let x(z)=...", they go on to say things about x. It may not be the final solution, but it may be used to find the solution. The two solutions may start with different x's and do something different to each to derive the same final answer. Are you sure that there is not more in those solutions than the first parts you are showing?
 

What is the difference between convergence and divergence of x(n)?

Convergence and divergence refer to the behavior of a sequence of numbers, x(n), as n (the index of the sequence) approaches infinity. Convergence means that the values of x(n) get closer and closer to a particular number, called the limit, as n gets larger. Divergence means that the values of x(n) do not approach a limit and instead either increase or decrease without bound.

How can I determine if a sequence x(n) is convergent or divergent?

To determine if a sequence is convergent, you can use the limit test, which states that if the limit of x(n) as n approaches infinity exists and is a finite number, then the sequence is convergent. To determine if a sequence is divergent, you can use the divergence test, which states that if the limit of x(n) as n approaches infinity does not exist or is infinite, then the sequence is divergent.

What is an example of a convergent sequence?

An example of a convergent sequence is the sequence 1/n, where n is the index. As n gets larger, the values of 1/n get closer and closer to 0, which is the limit of the sequence.

What is an example of a divergent sequence?

An example of a divergent sequence is the sequence (-1)^n, where n is the index. As n gets larger, the values of (-1)^n alternate between -1 and 1, never approaching a limit. Therefore, this sequence is divergent.

Can a sequence be both convergent and divergent?

No, a sequence cannot be both convergent and divergent. A sequence must exhibit either convergence or divergence behavior, but not both. If a sequence satisfies the conditions for both convergence and divergence, it is called oscillating and does not have a limit.

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