Products and Sums

The problem examines the theorem that if the product of    n    positive real numbers is  1,   then the sum is greater than or equal to  1.


Clearly, the proof of   3   implies the first two.

Looking at the first as a separate problem, however, 3 different ways to approach the Proof: 

HINT:    Use the AM-GM Inequality to prove problems 2  and  3.