7. Let an infinite geometric sequence $\left\{a_{n}\right\}$, with common ratio $q$, and $|q|<1, a_{1}=1, a_{n}=$ $k\left(a_{n+1}+a_{n+2}+\cdots\right)$, the range of the real number $k$ is $\qquad$ .
7. $k0$.

Since $a_{n+1}+a_{n+2}+\cdots=\frac{a_{n+1}}{1-q}=\frac{a_{n} q}{1-q}, a_{n}=k\left(a_{n+1}+a_{n+2}+\cdots\right)$, therefore $k=\frac{1-q}{q}=\frac{1}{q}-1$ and $-10$.