Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of random variables where \(X_{n}\) is an ExPo\(\operatorname{NENTIAL}\left(\theta+n^{-1}ight)\) random variable for all \(n \in \mathbb{N}\) where \(\theta\) is a positive real constant. Let \(X\) be an \(\operatorname{Exponential}(\theta)\) random variable. Prove that \(X_{n} \xrightarrow{d} X\) as \(n ightarrow \infty\).