am trying to show the following:
ILet $\xi_1,\xi_2,...$ be a sequence of independent identically distributed random variables with zero mean and finite and nonzero variance. Prove that the distributions of$ \frac{\sum_{i=1}^{n} \xi_i}{(\sum_{i=1}^{n} \xi_i^2)^{\frac{1}{2}}}$converge weakly to $N(0, 1)$ distribution as $n \to \infty$.
I think this might be an application of the Lyapunov CLT formulation, but I'm not sure if it's straightforward how to show that the Lyapunov Condition holds. I'm not really sure how to proceed.