... how can this infinite sum can be computed: $\sum_{k=1}^{\infty} a^k/(1-bc^k)$, with $0<a,b,c<1$?
Thanks.
https://www.wolframalpha.com/input/?...infinity%7D%5D
Here is what Wolframalpha comes up with when I put $a=0.5, b=0.125, c=0.25$. It is using the q-digamma function (which I have no idea what that even is). This is only giving you partial sums, so you would need to calculate the limit function as $n\to \infty$.