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## Main Question or Discussion Point

This is related to my senior design project.

I was wondering what would be a good way to check if a sequence is converging. As an example, imagine I have the following:

for n = 1:10,000

x(n) = f(n,n-1)

end

What I'm trying to say is that the sequence is updated in each iteration, and that the value of each sequence element is a function of present and past inputs. I know that the sequence is converging. Lets say that it is converging to zero. However, the sequence may oscillate like crazy, and cross zero many times, but eventually it will settle.

As of now, I have some hack code that basically computes the moving average. If the moving average gets to some threshold (i.e. not changing much), then I keep checking to see if it drops below some other threshold.

I was wondering what would be a good way to check if a sequence is converging. As an example, imagine I have the following:

for n = 1:10,000

x(n) = f(n,n-1)

end

What I'm trying to say is that the sequence is updated in each iteration, and that the value of each sequence element is a function of present and past inputs. I know that the sequence is converging. Lets say that it is converging to zero. However, the sequence may oscillate like crazy, and cross zero many times, but eventually it will settle.

**My question:**

How can I check if a sequence is converging to zero? What are some standard tests that I can look into?

How can I check if a sequence is converging to zero? What are some standard tests that I can look into?

As of now, I have some hack code that basically computes the moving average. If the moving average gets to some threshold (i.e. not changing much), then I keep checking to see if it drops below some other threshold.