Suppose that \(\left\{X_{n}ight\}_{n=1}^{\infty}\) is a sequence of random variables such that \(X_{n} \xrightarrow{r} X\) as \(n ightarrow \infty\) for some random variable \(X\). Prove that for \(r>1\) that

\[\lim _{n ightarrow \infty} E\left(\left|X_{n}ight|^{r}ight)=E\left(|X|^{r}ight) .\]