Is there any way of solving explicitly the limit of the series
$\sum_{n=0}^\infty q^n a^{p ^ n}$
where $0 and $a>0$? The series is obviously convergent as $a^{p ^ n} < \max(a,1)$ and so you can bound it by a standard geometric series, but it would be helpful to have an exact expression for it as well. Thanks very much!