Geometric series with modified terms

kop442000

I am looking for a way to sum some numbers. I understand that if I want to sum pⁱ, I can use the geometric series:

[itex]\sum\limits_{i=0}^N p^{i} = \frac{1-p^{N+1}}{1-p}[/itex]

But can anyone help me with what to do when I need:

[itex]\sum\limits_{i=0}^N p^{i} q^{ti}[/itex]

where t is just a constant.

Thank you in advance of any help!

JJacquelin

Let : [itex] P = p.q^{t}[/itex]