Sum over k of r-kt choose k by z^k

Theorem
Let $n \in \Z_{\ge 0}$ be a non-negative integer.

Then:


 * $\displaystyle \sum_k \dbinom {r - t k} k z^k = \frac {x^{r + 1} } {\left({t + 1}\right)x - t}$

where $\dbinom {r - t k} k$ denotes a binomial coefficient.