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[tex]\limsup \frac{S_n}{n} =\infty[/tex] and [tex]\liminf \frac{S_n}{n} = -\infty[/tex] almost surely.

I've managed to use the Borel-Cantelli lemma to show that [tex]P(|X_n| \geq n \text{ infinitely often}) = 1[/tex], but I can't pass to the lim sup/inf. Any help/suggestions would be appreciated.