Solution
= Solution
Because $(a_n)$ is a <monotone sequence>, every one of its first $n$ terms is at most $a_n$, so
$$
s_n\leq a_n.
$$
On the other hand, every term from $a_n$ through $a_{2n}$ is at least $a_n$, and hence
$$
a_n\leq\frac1{n+1}\sum_{k=n}^{2n}a_k
=\frac{2n s_{2n}-(n-1)s_{n-1}}{n+1}.
$$
Both the lower bound and upper bound tend to $x$ because the <Cesaro means> converge to $x$. The <squeeze theorem> gives
$$
\boxed{a_n\longrightarrow x}.
$$