Question 3
Suppose
$$\frac{a_1}{a_2^2}=\frac{a_2}{a_3^2}=\frac{a_3}{a_4^2}=\cdots=\frac{a_{2023}}{a_{2024}^2}=\frac{a_{2024}}{a_1^2}.$$
Evaluate
$$V=\frac{(a_1+a_2+\cdots+a_{2024})^2}{a_1^2+a_2^2+\cdots+a_{2024}^2}.$$
Assume all the displayed ratios are defined.
$$\frac{a_1}{a_2^2}=\frac{a_2}{a_3^2}=\frac{a_3}{a_4^2}=\cdots=\frac{a_{2023}}{a_{2024}^2}=\frac{a_{2024}}{a_1^2}.$$
Evaluate
$$V=\frac{(a_1+a_2+\cdots+a_{2024})^2}{a_1^2+a_2^2+\cdots+a_{2024}^2}.$$
Assume all the displayed ratios are defined.