1. Given point $G$ is the centroid of $\triangle A B C$, and $\overrightarrow{A B}=\boldsymbol{a}, \overrightarrow{A C}=\boldsymbol{b}$. If $P Q$ passes through point $G$ and intersects $A B, A C$ at points $P, Q$, and $\overrightarrow{A P}=m \boldsymbol{a}, \overrightarrow{A Q}=n \boldsymbol{b}$, then $\frac{1}{m}+\frac{1}{n}=$ $\qquad$ .
1. 3 Detailed Explanation: Special Value Method. When $P Q // B C$, $m=n=\frac{2}{3}$, thus $\frac{1}{m}+\frac{1}{n}=3$.