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Limit calculation

  1. Aug 16, 2005 #1
    Dear members,

    I am calculating the following limit:

    [tex]
    \lim_{t\rightarrow \infty} \sum_{k=1}^{t-2} \frac{\lambda^{t-k-1}}{k}
    [/tex]
    where
    [tex]
    0 < \lambda <1
    [/tex]

    Does any body know how to do it? Thanks a lot!
     
  2. jcsd
  3. Aug 16, 2005 #2
    A hint:

    [tex]0\leq \lim_{t\rightarrow \infty} \sum_{k=1}^{t-2} \frac{\lambda^{t-k-1}}{k}=\lim_{t\rightarrow \infty} \lambda^t \sum_{k=1}^{t-2} \frac{\lambda^{k-1}}{k} \leq \lim_{t\rightarrow \infty} \lambda^t \sum_{k=1}^{\infty} \frac{\lambda^{k-1}}{k}[/tex]
     
    Last edited by a moderator: Aug 16, 2005
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