Let $(X_n)_{n\in\mathbb{N}}$ be independent and \begin{equation} P(X_n=n)=P(X_n=-n)=\frac{1}{2}n^{-{\frac{5}{2}}}=\frac{1}{2}(1-P(X_n=0)), \ n\in\mathbb{N}. \end{equation} Show that $(X_n)_{n\in\mathbb{N}}$ satisfies the Strong Law of Large Numbers. My first guess was to use a Borel-Cantelli argument but I cant figure out how.
2026-04-13 23:50:26.1776124226
Sequence satisfies the strong law of large numbers
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