Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Is there any way of solving explicitly the limit of the series

$\sum_{n=0}^\infty q^n a^{p ^ n}$

where $0<p,q<1$ 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!

share|cite|improve this question
Eep, a nested exponential. I doubt this has a tidy closed form... – J. M. Jan 26 '12 at 16:17
Tidy or not, I'm pretty sure there is no closed form except in the trivial case $a=1$. – Robert Israel Jan 27 '12 at 0:12

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.