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)

Thanks in advance!