Let \(\left\{c_{n}ight\}_{n=1}^{\infty}\) be a sequence of real constants such that

\[\lim _{n ightarrow \infty} c_{n}=c\]

for some constant \(c \in \mathbb{R}\). Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of random variables such that \(P\left(X_{n}=c_{n}ight)=1-n^{-1}\) and \(P\left(X_{n}=0ight)=n^{-1}\). Prove that \(X_{n} \xrightarrow{p} c\) as \(n ightarrow \infty\).