= Solution
{c}
Choose $N$ beyond every <peak of a sequence> of both $(a_n)$ and $(-a_n)$. Every term with index at least $N$ has a strictly larger later term and a strictly smaller later term.
Suppose for a contradiction that $a_n\to L$. Starting at $a_N$, recursively select a strictly increasing <subsequence> and a strictly decreasing <subsequence>. Both must have <limit of a sequence> $L$. If their second terms are $u>a_N$ and $v<a_N$, respectively, passage to their <limits of sequences> gives
$$
L\geq u>a_N,\qquad L\leq v<a_N,
$$
a contradiction. Hence \b[$(a_n)$ does not converge.] This argument includes the possibility that either <set> of <peaks of a sequence> is empty.
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