= Solution
{c}
For each positive integer $m$, the events $\{|X_n|\geq mn\}$ are independent and have divergent total probability by part (i). The <Borel-Cantelli second lemma> makes them occur infinitely often. Taking the countable intersection over $m$ gives
$$
\boxed{\limsup_n|X_n|/n=\infty\quad\text{almost surely}.}
$$
If $\limsup_n|S_n|/n$ were finite along any such sample path, then for some finite path-dependent $C$, $|S_n|\leq Cn$ eventually. But $X_n=S_n-S_{n-1}$ would give $|X_n|/n\leq C+C(n-1)/n\leq2C$ eventually, a contradiction. Therefore
$$
\boxed{\limsup_n|S_n|/n=\infty\quad\text{almost surely}.}
$$
This is the <divergence of normalized iid partial sums without a first absolute moment>.
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