2020 IMO 第 2 题

Let $a \geq b \geq c \geq d > 0$ be real numbers satisfying $a + b + c + d = 1$ . Prove that

$$(a + 2b + 3c + 4d)a^{a}b^{b}c^{c}d^{d}< 1.$$

设 $a \geq b \geq c \geq d > 0$ 为满足 $a + b + c + d = 1$ 的实数。证明

$$(a + 2b + 3c + 4d)a^{a}b^{b}c^{c}d^{d}< 1。$$