This is a problem after the section "Strong Law of Large Numbers" of Shiryaev's Probability:
Let $\xi_1,\xi_2,...$ denote independent and identically distributed random variables such thatt $E|\xi_1|=\infty$. Show that $$\limsup_{n\to\infty}\left|\frac{S_n}{n}-a_n\right|=\infty\text{ (P-a.s.)}$$ for every sequence of constants $\{a_n\}$.
I have no idea about it. Any hint please. Thanks!