4. Given a geometric sequence $\left\{a_{n}\right\}$ satisfies
$$
\lim _{n \rightarrow \infty}\left(a_{1}+a_{2}+\cdots+a_{n}\right)=-2 \text {. }
$$

Then the range of values for $a_{1}$ is $\qquad$
4. $(-4,-2) \cup(-2,0)$.

Let $\left\{a_{n}\right\}$ be a geometric sequence with common ratio $q$.
From the existence of the limit of partial sums, we have
$$
\left\{\begin{array}{l}
0<|q|<1, \\
\frac{a_{1}}{1-q}=-2 .
\end{array}\right.
$$

Then $0<\left|a_{1}+2\right|<2$.
Solving this, we get $a_{1} \in(-4,-2) \cup(-2,0)$.