Construct dependent random variables which converge to standard normal

Question

I'm asked to construct dependent random variables $X_n, n \in \mathbb{N}$, such that

$$\frac{1}{\sqrt{N}} \sum_{k=1}^N X_k$$

converges in distribution to $\mathcal{N}(0, 1)$ as $N \rightarrow \infty$. I honestly don't know where to start. Should I approach the problem with identically distributed variables?

Answer 1

Consider $(X_1,X_1,X_2,X_3,...)$ where $\{X_n\}$ is i.i.d with standard nomal distribution. This sequence is not independent. [ See my comment above].