The Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, . . . . In general, the Fibonacci numbers are defined by f1 = 1, f2 = 1, and for n ≥ 3, fn = fn–1 + fn–2. Prove that the nth Fibonacci number fn satisfies fn < 2n.
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