Question 52
Let $a_{1} \geq a_{2} \geq \cdots \geq a_{n}\gt 0$ be real numbers. Prove that
$$
a_{1} a_{2}\left(a_{1}-a_{2}\right)+a_{2} a_{3}\left(a_{2}-a_{3}\right)+\cdots+a_{n-1} a_{n}\left(a_{n-1}-a_{n}\right) \geq a_{1} a_{n}\left(a_{1}-a_{n}\right) .
$$
$$
a_{1} a_{2}\left(a_{1}-a_{2}\right)+a_{2} a_{3}\left(a_{2}-a_{3}\right)+\cdots+a_{n-1} a_{n}\left(a_{n-1}-a_{n}\right) \geq a_{1} a_{n}\left(a_{1}-a_{n}\right) .
$$