Consider $X_i$'s as iid random variables with mean 0 that are not point mass (they are non-degenerate) and they have finite variance. $a_i$'s are constants that are finite which converge to $0$. How can I show that that $\sum_{i = 1}^{n} a_iX_i /\sqrt{n} \rightarrow 0$ in distribution?
Thank you