Let $n \in \Bbb{N}$. Let $x_1,x_2,\ldots,x_n$ be positive real numbers such that $\prod_{i=1}^n x_i = 1$. Prove that $\sum_{i=1}^n x_i \ge n $
Prove that $a_1+\cdots+a_n \geq n$ if $a_1$, $a_2$, ... $a_n$ are positive real numbers and their product is $1$