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Math Help - Cauchy's convergence test

  1. #1
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    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)


    Thanks in advance!
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  2. #2
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    Quote Originally Posted by Darkprince View Post
    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




    Thanks in advance!
    .
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  3. #3
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    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.
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