CLT for pairwise differences

Let $\{X_{n}\}_{n\ge 1}$ be a sequence of i.i.d. random variables such that $E(X_{i})=1$ and $\operatorname{Var}(X_{i})=1$, $i=1,2,…$. Then the approximate distribution of $\dfrac{1}{\sqrt{n}}\sum_{i=1}^{n}\left(X_{2i}-X_{2i-1}\right)$, for large $n$, is