= Solution
{c}
For a <series> of <complex numbers>, form the <partial sums> $S_N=\sum_{n=1}^Na_n$. The <series> converges when these <partial sums> have a finite <limit of a sequence> $S\in\mathbb C$:
$$
\boxed{\forall\varepsilon>0\ \exists N_0\ \forall N\geq N_0:\quad |S_N-S|<\varepsilon.}
$$
The <series> has <absolute convergence> when $\sum_{n=1}^{\infty}|a_n|$ converges as a <series> of nonnegative <real numbers>. A <series> beginning at $n=0$ uses the same definitions with that starting index.
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