Limit calculation

  • Thread starter phonic
  • Start date
  • #1
phonic
28
0
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 anybody know how to do it? Thanks a lot!
 

Answers and Replies

  • #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:

Suggested for: Limit calculation

  • Last Post
Replies
29
Views
486
  • Last Post
Replies
11
Views
580
  • Last Post
Replies
2
Views
82
  • Last Post
Replies
8
Views
394
  • Last Post
Replies
3
Views
402
  • Last Post
Replies
3
Views
574
  • Last Post
Replies
3
Views
607
  • Last Post
Replies
1
Views
437
  • Last Post
Replies
6
Views
499
  • Last Post
Replies
5
Views
594
Top