Question 164
Let $a$, $b$, and $c$ be positive real numbers such that
$$
a b c = 1
$$
Prove that for every positive integer $n$,
$$
a + b + c \gt \frac{1}{a} + \frac{1}{b} + \frac{1}{c} .
$$
$$
a b c = 1
$$
Prove that for every positive integer $n$,
$$
a + b + c \gt \frac{1}{a} + \frac{1}{b} + \frac{1}{c} .
$$