= Solution
{c}
The summands are nonnegative, so <monotone convergence theorem>, equivalently <Tonelli's theorem> for a sum, gives
$$
\mathbb E\sum_{n=1}^\infty\left(\frac{S_n}{n}\right)^4
=\sum_{n=1}^\infty\frac{\mathbb ES_n^4}{n^4}
\leq3c^4\sum_{n=1}^\infty n^{-2}<\infty.
$$
A nonnegative <random variable> with finite <expected value> is finite almost surely. Thus the displayed nonnegative series converges almost surely, forcing its individual terms to tend to zero. Taking fourth roots proves
$$
\boxed{\frac1n\sum_{k=1}^nX_k\longrightarrow0
\quad\text{almost surely}.}
$$
This is a fourth-moment proof of a <strong law of large numbers> for these bounded independent variables, without an identical-distribution assumption.
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