If $X_{1}$, $X_{2} \cdots X_{2n}$ be iid $\mathcal{N}(0,1)$ random variables

Question

If $X_{1}$, $X_{2} \cdots X_{2n}$ be iid $\mathcal{N}(0,1)$ random variables. lET $U_{n}=\frac{X_{1}}{X_{2}}+\frac{X_{3}}{X_{4}}+ \cdots \frac{X_{2n-1}}{X_{2n}}$ and $V_{n}=X_{1}^{2}+ \cdots X_{n}^{2}$. Find the limiting distribution of $Z_{n}=\frac{U_{n}}{V_{n}}$. I know that by the weak law of large numbers $\frac{1}{n}V_{n}$ converges to $0$, and hence it does not allow me to us slutsky's theorem. Any hints?