Infinite Series arising in Laplace transform

Question

I'm trying to understand how the answer was computed for the following infinite series:

$\sum _ { x = 1 } ^ { \infty } e ^ { - s x } p q ^ { x - 1 } = \frac { p e ^ { - s } } { 1 - q e ^ { - s } }$

Any help would be highly appreciated.

Answer 1

Hint: $e^{-sx}pq^{x-1}=(e^{-s}q)^{x-1} \cdot pe^{-s}$. You know the sum of a geometric series, right?