Question

Prove that 3n< n! if n is an integer greater than 6.

Answer 1

Let $n=7$. Then

$3(7)=21$

Assume the inequality holds for $n=k$, so that $3k$. Then for $n=k+1$, you have, for $k>7$,

$3(k+1)$

so the statement is true.