Question 1
Let $a_1, a_2, \dots, a_{14}$ be some positive real numbers. Prove that
$$
\frac{a_1}{a_2+a_3} + \frac{a_2}{a_3+a_4} + \dots + \frac{a_{14}}{a_1+a_2} \ge \frac{a_1}{a_{14}+a_1} + \frac{a_2}{a_1+a_2} + \dots + \frac{a_{14}}{a_{13}+a_{14}}.
$$
When does the equality occur?
$$
\frac{a_1}{a_2+a_3} + \frac{a_2}{a_3+a_4} + \dots + \frac{a_{14}}{a_1+a_2} \ge \frac{a_1}{a_{14}+a_1} + \frac{a_2}{a_1+a_2} + \dots + \frac{a_{14}}{a_{13}+a_{14}}.
$$
When does the equality occur?