# Cauchy's convergence test

• Mar 15th 2011, 11:25 AM
Darkprince
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)

• Mar 15th 2011, 12:18 PM
tonio
Quote:

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