 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

\b[False.] Take the positive <sequence> $\boxed{a_n=n}$. Then
$$
\frac{a_{n+1}}{a_n}=\frac{n+1}{n}=1+\frac1n\longrightarrow1,
$$
but $a_n\to+\infty$, so it has no finite <limit of a sequence>. Successive ratios close to one do not prevent cumulative growth.

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