$1$ point$)$ Prove that n$!$ n for any integer n $1$ Proof by Induction: Base Case: $($n $1)$ LS Thus the base case holds for n $1$ Inductive Hypothesis: Suppose n$\text{'}<$ nn is true for some n k $>1,$ that is k$!<$ kk Inductive Step: Prove that n$!$ nn is true for n$-$k $+1,$ that is k$1)($k$1)*$ by the inductive hypothesis We have Therefore, by the principle of mathematical induction, n$!"$ for any integer n $21$ A$.$ k$*($k$1$ D$\mathrm{.}22$ G$.1$