1. If the 5th term in the expansion of $\left(x \sqrt{x}-\frac{1}{x}\right)^{6}$ is $\frac{15}{2}$, then $\lim _{n \rightarrow \infty}\left(x^{-1}+x^{-2}+\cdots+x^{-n}\right)=$
1. $\because T_{5}=C_{6}^{1}(x \sqrt{x})^{2} \cdot\left(-\frac{1}{x}\right)^{4}=\frac{15}{x}$, from $\frac{15}{x}=\frac{15}{2}$, we get $x^{-1}=\frac{1}{2}$. Therefore, $\lim _{n \rightarrow \infty}\left(x^{-1}+x^{-2}+\cdots+x^{-n}\right)=\frac{\frac{1}{2}}{1-\frac{1}{2}}=1$.