# Thread: Cauchy's convergence test

1. ## Cauchy's convergence test

Hello, I want to ask about the Cauchy's convergence test. It states that for every epsilon<0 there is a number, such that for all [I]n, m > N holds abs(sm-sn)<epsilon.
My question is how small should be epsilon for the convergence test to be valid?
i.e I have the series x(n+1)=(x(n))^3-a*x(n)

2. Originally Posted by Darkprince
Hello, I want to ask about the Cauchy's convergence test. It states that for every epsilon<0 there is a number, such that for all [I]n, m > N holds abs(sm-sn)<epsilon.
My question is how small should be epsilon for the convergence test to be valid?

Uuh? The test is very clear: the Cauchy condition must be fulfilled for every , and thus for any,

positive epsilon.

i.e I have the series x(n+1)=(x(n))^3-a*x(n)

Why do you call that "series"?? And if you meant "sequence", the only thing you've got is

a sequence defined recursively...so?

Tonio

.

3. I want to check this sequence's behavior as n goes to infinity and by choosing x1 and a. I have to do it using iterations using a Matlab script and I am thinking to use Cauchy's convergence test and choosing an arbitrarily small epsilon. I don't have any other idea.