Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of random variables that converge in \(r^{\text {th }}\) mean to a random variable \(X\) as \(n ightarrow \infty\) for some \(r>0\). Prove that if

\[\sum_{n=1}^{\infty} E\left(\left|X_{n}-Xight|^{r}ight)<\infty\]

then \(X_{n} \xrightarrow{\text { a.c. }} X\) as \(n ightarrow \infty\).