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Math Help - sequence analysis

  1. #1
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    sequence analysis

    I have a number of sequences for which i have to analyse the given sequence, the part i'm having difficulty with is determining if it's cauchy and the sup/inf and limsup and liminf, normally i have a good idea if it is or isnt cauchy but am unsure how to show it.

    For example how do i show if ;

    n/n(n+1) is cauchy and then how do i show the limsup and liminf,

    any help would be greatly appreciated i'm stuck here bigtime.

    Cheers
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  2. #2
    MHF Contributor

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    Quote Originally Posted by monster View Post
    I have a number of sequences for which i have to analyse the given sequence, the part i'm having difficulty with is determining if it's cauchy and the sup/inf and limsup and liminf, normally i have a good idea if it is or isnt cauchy but am unsure how to show it.

    For example how do i show if ;

    n/n(n+1) is cauchy and then how do i show the limsup and liminf,

    any help would be greatly appreciated i'm stuck here bigtime.

    Cheers
    I presume you mean \frac{n}{n(n+1)}.

    Surely you can see that this sequence converges to 0? Since it converges, it is Cauchy and liminf and limsup are both equal to the limit of the sequence.
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  3. #3
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    yep, i can see this converges to 0 but is this all i need to do to show it's Cauchy, and if a sequence does not converge is it always non cauchy?
    I have been getting bogged down in the complicated definition of the cauchy sequence
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