Question 70
Let $n \ge 3$ be an integer, and let $a_2, a_3, \dots, a_n$ be positive real numbers such that $a_2 a_3 \dots a_n = 1$. Prove that
$$
(1 + a_2)^2 (1 + a_3)^3 \dots (1 + a_n)^n \gt n^n.
$$
$$
(1 + a_2)^2 (1 + a_3)^3 \dots (1 + a_n)^n \gt n^n.
$$