I am stuck with the question below,
Prove by mathematical induction that $n
I am stuck with the question below,
Prove by mathematical induction that $n
First, for $n=3$ you have $3< 3!=6 $. Suppose that for some $k$ it holds that $k
If this is homework and the professor specifically said to use induction, then disregard this answer, I suppose. Otherwise, the statement can be proven directly without induction.
Given any $n \geq 3$, we can write $n! = n(n-1)!$ and be confident that $n-1 \geq 2$ (so we aren't making inappropriate use of $0!$). From this expression, it is clear that $n! > n$, since $n!$ is equal to $n$ times some number strictly greater than 1.