Infinte sum - standard result?

[yaboidjaf]

Hi, I'm working on a continuous time random walk problem, but my question is to do with analysis.
I have and infinite sum and am unsure how to get form one step to the next or whether it is just a standard result.
The variables aren't important but it looks like

sum from n=0 to inf of (p^n((1-p)/s)(cos(ka))^n) = ((1-p)/s)(1/(1-pcos(ka))

sorry it looks messy but i was struggling with the latex.
Is this a standard result or is there a trick I can apply?
Thanks

 

[Deadstar]

See here.

http://en.wikipedia.org/wiki/Geometric_series#Formula

It's just the geometric series with,

$$a = \frac{1-p}{s}$$

and

$$r^n = \bigg{(}\frac{p}{\cos(ka)}\bigg{)}^n$$

(make sure you use the formula for when n goes to infinity, i.e. the s = ... one)

 

[yaboidjaf]

brilliant, thanks a lot!