 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

The <binomial theorem> gives $\binom{2n}{n}\leq\sum_{k=0}^{2n}\binom{2n}{k}=4^n$. Therefore
$$
\left|\binom{2n}{n}3^{-2n}\sin n\right|\leq(4/9)^n.
$$
The <geometric series> with ratio $4/9$ converges. By the <comparison test>, the given <series> is \b[absolutely convergent].

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