Let (left{X_{n}ight}_{n=1}^{infty}) be a sequence of random variables where for each (n in mathbb{N}, X_{n}) has an

Question:

Let $\left\{X_{n}ight\}_{n=1}^{\infty}$ be a sequence of random variables where for each $n \in \mathbb{N}, X_{n}$ has an BERNoulli $\left[\frac{1}{2}+(n+2)^{-1}ight]$ distribution, and let $X$ be a BERNOulli $\left(\frac{1}{2}ight)$ random variable. Prove that $X_{n} \xrightarrow{d} X$ as $n ightarrow \infty$.

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