= Solution
{c}
A <sequence> $(a_n)$ has <limit of a sequence> $L$ if
$$
\forall\varepsilon>0\ \exists N\in\mathbb N\ \forall n\geq N:\quad |a_n-L|<\varepsilon.
$$
For the reciprocal rule, the required condition is $\boxed{L\ne0}$. Indeed, eventually $|a_n-L|<|L|/2$, so $|a_n|\geq|L|/2>0$. The reciprocals are then defined on this tail, and
$$
\left|\frac1{a_n}-\frac1L\right|=\frac{|a_n-L|}{|a_n||L|}\leq\frac{2|a_n-L|}{|L|^2}\longrightarrow0.
$$
A finite number of zero initial terms does not affect this tail <limit of a sequence>; if a reciprocal <sequence> is required at every index, those terms must be excluded or assigned arbitrary values separately.
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