# Prove that 3 raised to power n is strictly less than n! for any nat...

## Question

Prove that 3 raised to power n is strictly less than n! for any natural number n which is greater than or equal to 7.

## Solution Preview

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Induction claim P(n): 3^n < n! for all n ≥7.
Base case: P(7): 3^7< 7! => 2,187 < 5,140 true
General Case: We assume P(n) is true for all m≤n and we must prove it for m=n+1, thus...

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