Summation of geometric progression like sequence

euvtl · P versus NP Offline Joined: 16 Aug 2004 Posts: 40

$S(x, m, n) = \sum_{i = 0}^{n}x^{m^{i}} = x + x^m + x^{m^{2}} + ... + x^{m^{n}}$

Is there a closed form formula for $S(x, m, n)$ in terms of $\{x, m, n\}$ ? May be a generating function?
This looks like a GP but obviously it isn't. Ratio of consecutive terms is dependent on both $x$ and $m$ .

Note: I remember seeing something similar here on ML but I couldn't find it using search...

**Posted:** Fri Oct 05, 2007 9:00 pm