Analysis problem (sequences)-please help

  1. Analysis problem (sequences)--please help

    Here is the definition:

    t_n = [s_1 + s_2 + ... + s_n] / n ; n >/= 1

    I have to show that if lim n-> [infinity] s_n = s, then lim n-> [infinity] t_n = s

    First of all, I don't think it's true. Because if s is finite, then lim s/n as n-> [infinity] would be zero, right? And thus lim t_n as n-> [infinity] is zero, and they're not the same.

    I'm just wondering how to go about this problem. Thank you.
  2. jcsd
  3. Hurkyl

    Hurkyl 15,987
    Staff Emeritus
    Science Advisor
    Gold Member

    I think I would try it directly with the epsilon-delta definition of a limit.

    BTW, you should be able to convince yourself that the limit of t_n is not always zero by considering a simple example.
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