For skewness, take the limit of the skewness result above
\begin{equation*}
\lim_{n \rightarrow \infty} \frac{n(2p-1)(p-1)p}{(-n(p1)p)^{3/2}} = \lim_{n \rightarrow \infty} C \frac{n}{n^{3/2}} = 0.
\end{equation*}
Similarly for kurtosis
\begin{equation*}
\lim_{n \rightarrow \infty} -\frac{6p^2 - 6p + 1}{n (p - 1) p} +3 = 0 + 3 = 3.
\end{equation*}