1. In the geometric sequence $\left\{a_{n}\right\}$, $a_{2}=\sqrt{2}, a_{3}=\sqrt[3]{3}$, then the value of $\frac{a_{1}+a_{2011}}{a_{7}+a_{2017}}$ is
Answer: $\frac{8}{9}$.
Solution: The common ratio of the sequence $\left\{a_{n}\right\}$ is $q=\frac{a_{3}}{a_{2}}=\frac{\sqrt[3]{3}}{\sqrt{2}}$, so $\frac{a_{1}+a_{2011}}{a_{7}+a_{2017}}=\frac{a_{1}+a_{2011}}{q^{6}\left(a_{1}+a_{2011}\right)}=\frac{1}{q^{6}}=\frac{8}{9}$.