Proof
For skewness, take the limit of the skewness result above
\begin{equation*}
\lim_{r \rightarrow \infty} \frac{2-p}{\sqrt{r(1-p)}} = lim_{r \rightarrow \infty} \frac{C}{r^{1/2}} = 0.
\end{equation*}
Similarly for kurtosis
\begin{equation*}
\lim_{r \rightarrow \infty} \frac{p^2-6p+6}{r(1-p)} + 3 = lim_{r \rightarrow \infty} \frac{C}{r} + 3 = 3.
\end{equation*}