3. If the 5th term in the expansion of $\left(x \sqrt{x}-\frac{1}{x}\right)^{6}$ is 5, then $\lim _{n \rightarrow \infty}\left(x^{-1}+x^{-3}+\cdots+x^{1-2 n}\right)$ equals ( ).
A. $\frac{3}{8}$
B. $\frac{9}{8}$
C. 1
D. $\frac{1}{2}$
3. A. From $T_{4+1}=C_{6}^{4}(x \sqrt{x})^{2} \cdot\left(-\frac{1}{x}\right)^{4}=5$, we get $x^{-1}=\frac{1}{3}, x^{-3}=\left(\frac{1}{3}\right)^{-3}$, thus $\lim _{n \rightarrow \infty}\left(x^{-1}+\cdots+x^{1-2 n}\right)=$ $\frac{x^{-1}}{1-x^{-2}}=\frac{3}{8}$