Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of independent random variables where \(X_{n}\) has a \(\operatorname{BETA}\left(\alpha_{n}, \beta_{n}ight)\) distribution for all \(n \in \mathbb{N}\), where \(\left\{\alpha_{n}ight\}_{n=1}^{\infty}\) and \(\left\{\beta_{n}ight\}_{n=1}^{\infty}\) are sequences of real numbers such that \(\alpha_{n}>0\) and \(\beta_{n}>0\) for all \(n \in \mathbb{N}\). Find the necessary properties for the sequences \(\left\{\alpha_{n}ight\}_{n=1}^{\infty}\), and \(\left\{\beta_{n}ight\}_{n=1}^{\infty}\) that will ensure that \(\left\{X_{n}ight\}_{n=1}^{\infty}\) is uniformly integrable.