If the product of n positive numbers is unity, then their sum is

The problem is a direct application of the Arithmetic Mean-Geometric Mean (AM-GM) inequality. This inequality states that for any set of n positive real numbers, their arithmetic mean is always greater than or equal to their geometric mean. Mathematically, (a1 + a2 +... + an) / n ≥ (a1 * a2 *... * an)^(1/n). Given that the product of the n positive numbers is unity (1), the geometric mean becomes the nth root of 1, which is 1. Substituting this into the inequality gives (Sum) / n ≥ 1, which simplifies to Sum ≥ n. Therefore, the sum of n positive numbers whose product is unity is never less than n. Equality (Sum = n) occurs only when all the numbers are equal to 1.