Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of random variables such that \(X_{n}\) has a UNI\(\operatorname{FORM}\left\{0, n^{-1}, 2 n^{-2}, \ldots, 1ight\}\) distribution for all \(n \in \mathbb{N}\). Prove that \(X_{n} \xrightarrow{d} X\) as \(n ightarrow \infty\) where \(X\) has a UnIFORm \([0,1]\) distribution.