I am rather new to mathematical induction. Specially inequalities, as seen here How to use mathematical induction with inequalities?. Thanks to that question, I've been able to solve some of the form $ 1 + \frac{1}{2} + \frac{1}{3} + \cdots + \frac{1}{n} \leq \frac{n}{2} + 1 $.
Now, I was presented this, for $n \ge 4$:
$$2^n I tried to do it with similar logic as the one suggested there. This is what I did: Prove it for $n = 4$:
$$2^4 = 16$$
$$4! = 1\cdot2\cdot3\cdot4 = 24$$
$$16 < 24$$
Assume the following:
$$2^n Even though the procedure seems to be right, I wonder: