I3.1 If the product of numbers in the sequence $10^{\frac{1}{11}}, 10^{\frac{2}{11}}, 10^{\frac{3}{11}}, \ldots, 10^{\frac{\alpha}{11}}$ is 1000000 , determine the value of the positive integer $\alpha$.
$\begin{array}{l}10^{\frac{1}{11}} \times 10^{\frac{2}{11}} \times 10^{\frac{3}{11}} \times \ldots \times 10^{\frac{\alpha}{11}}=10^{6} \\ \frac{1}{11}+\frac{2}{11}+\frac{3}{11}+\cdots+\frac{\alpha}{11}=6 \\ \frac{1}{2}(1+\alpha) \alpha=66 \\ \alpha^{2}+\alpha-132=0 \\ (\alpha-11)(\alpha+12)=0 \\ \alpha=11\end{array}$