For skewness, take the limit of the skewness result above as \(n_1, n_2\text{,}\) and \(r\) are uniformly increased together (i.e. all are doubled, tripled, etc.) To model this behavior one can simply scale each of those term by some variable \(k\) and then let \(k\) increase. Asymptotically, the result is
\begin{equation*}
\lim_{k \rightarrow \infty} \frac{(nk-2n_1k)(nk-1)^{1/2}(nk-2rk)}{rkn_1k(nk-n_1k)(nk-rk)^{1/2}(nk-2)} ~ \lim_{k \rightarrow \infty} C \frac{k^{5/2}}{k^{9/2}}= 0.
\end{equation*}
Similarly for kurtosis. However, since we can’t find a nice formula for the kurtosis then taking the limit can be difficult. So, we will have to appeal to general results proved in a course that would follow up this one that would prove this fact must be true. Sadly, not here.