Consider the simple random walk $(X_n)_{n \in \mathbb{N}}$ starting from $X_0 = 0$.
Consider $\varepsilon>0$, show that, for all $\delta>0$, $$ \lim _{n \rightarrow \infty} \mathbb{P}\left(\frac{\left|X_{n}\right|}{n^{\frac{1}{2}+\varepsilon}}>\delta\right)=0 . $$
I'm new to random walks in probability and don't know how to solve this.