Question

P(n): n! > 3n for n ≥ 7. What is the Base Step?

Answer 1

Let $P(n): n! > 3n$ for $n ≥ 7$. Since we prove that statement is true for all $n ≥ 7$, we conclude that the Base Step is for $n=7$, that is $P(7): 7! > 3\cdot 7$ which is equivalent to $5040>21.$