Sum of real numbers that multiply to 1

Question

I've seen a question in my math book with this explanation above it: "If the product of n positive real numbers is 1, then the sum of these numbers must be more than n". I was wondering if this is correct, and if it is, could someone give an explanation or a proof for it?

Answer 1

AM-GM, for $n$ in the positive reals, states $$\displaystyle\frac{\sum\limits^{n}_{i=1}a_i}{n}\ge \left(\prod^{n}_{i=1}{a_i}\right)^\frac{1}{n}$$

Answer 2

This is the AM-GM inequality.