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Math Help - Proof of that a limit -> 0 as n-> infinity

  1. #1
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    Proof of that a limit -> 0 as n-> infinity

    Hey,


    I've been trying to work out the following question,


    This is it including what I hope is an ok, or on the way to an ok proof.





    The book has a hint given that states there exists N in naturals such that |z_n|<ε/2 for all n>N so I kind of tried to use that to find a bound on w_n.


    Does this look okay?


    Thank you in advance,


    Jess
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  2. #2
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    Re: Proof of that a limit -> 0 as n-> infinity

    It is not true that for every ε there exists an N such that |zN+1+ ... +zₙ| < ε / 2 for all n > N. E.g., for zₙ = 1 / n, any tail zN+1 + zN+2 + ... is infinite.

    It is even less true that |z₁ + ... + zN| < ε / 2. For example, we could have z₁ = 100.
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  3. #3
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    Re: Proof of that a limit -> 0 as n-> infinity

    sweet thanks
    Last edited by Jesssa; August 22nd 2012 at 01:42 AM.
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