Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of random variables such that for each \(n \in \mathbb{N}\), \(X_{n}\) has a \(\operatorname{GAmma}\left(\alpha_{n}, \beta_{n}ight)\) distribution where \(\left\{\alpha_{n}ight\}_{n=1}^{\infty}\) and \(\left\{\beta_{n}ight\}_{n=1}^{\infty}\) are sequences of positive real numbers such that \(\alpha_{n} ightarrow \alpha\) and \(\beta_{n} ightarrow \beta\) as \(n ightarrow \infty\), some some positive real numbers \(\alpha\) and \(\beta\). Prove that \(X_{n} \xrightarrow{d} X\) as \(n ightarrow \infty\) where \(X\) has a \(\operatorname{Gamma}(\alpha, \beta)\) distribution.