Proof approach for $n! \ge (n/2)^{n/2}$
87813
How to show that for all k, $k! \ge (k/2)^{k/2}$
72735
Understanding the proof of a formula for $p^e\Vert n!$
136274
$n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
79847
proving of inequality $(n!)^2 \leq n^n\cdot n!\leq (2n!)$, where $n\in \mathbb{N}$
88838
How can I prove this inequality for $n\geq 2$?
72600
Proof that $n!\leq {(\frac{n+1}{2})}^{n}$
62177
Prove that: $2^n < n!$ Using Induction
121544
Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
2554
Show that if $n>2$, then $(n!)^2>n^n$.
35027
Need help with continuing an idea concerning showing that $4\sum\limits_{n \ge 1} a_n^2 \ge \sum\limits_{n \ge 1} \frac1{n^2}(a_1+...+a_n)^2 $
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
61117
Prove by induction: $n! \ge 2^{(n-1)}$ for any $n \ge 1$
27204
Proof for convergence of a given progression $a_n := n^n / n!$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
27580
Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction