1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?