The Fibonacci numbers, denoted fn, form a sequence such that f1 = 1, f2 = 1, and fn = fn1 + fn2 for n 3.

Let the Fibonacci-2 numbers gn be defined as follows: g1 = 2, g2 = 2, and gn+2 = gn+1gn for all n 1. Show that gn = 2fn for each natural number n.