Limit calculation

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Main Question or Discussion Point

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!
 

Answers and Replies

rachmaninoff
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]
 
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