Let \(x_{1}, x_{2}, \ldots, x_{k}\) be possible values of a random variable \(\xi\). Prove that as \(n \rightarrow \infty\)

(a) \(\frac{M \xi^{n+1}}{M \xi^{n}} \rightarrow \max _{1 \leqslant j \leqslant k} x_{j}\),

\[ \begin{equation*} \sqrt[n]{M \xi^{n}} \rightarrow \max _{1 \leqslant j \leqslant k} x_{j} \tag{b} \end{equation*} \]