Prove that the following limit is 0

Question

I have to prove this following statement.

Let $(X_n)_{n\in\Bbb N}$ a sequence of independent random variables with $\mathbf E(X_i) = 0$ and $\mathbf{Var}(X_i)=C<\infty$ for all $ i \in \Bbb >N $. Let $ p >1/2 $ and $S_n=X_1+...+X_n $.

Show that $ \lim_{n\to \infty}S_n/n^p =0$ in probability.

I think that I should use the central limit theorem, but I am not sure because this way does not lead me to something..

Thanks in advance