Comparing $n^n$ and $n!^2$
2554
Show that if $n>2$, then $(n!)^2>n^n$.
136274
$n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
20964
Proof that $n^2 < 2^n$
130093
Prove by Induction : $n < 2^n$
35611
How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?
144741
Does series $4^{n}×\frac{(n!)^2}{(2n)!}$ converge or diverge?
138304
getting tight bounds on n!
96845
Question: Compare the cardinality between the sets $\Bbb R$ and $\Bbb N^{\Bbb N}$
26316
Convergence of $a_n= \frac{n!}{n^n}$?
138905
Find the limit of $\log\Big(\frac{(n^2+n)!}{n^2!n^{2n}}\Big)$
126073
Radius of convergence of power series $\sum c_n x^{2n}$ and $\sum c_n x^{n^2}$
27204
Proof for convergence of a given progression $a_n := n^n / n!$
10191
Binomial theorem: divisibility by $n^2$
136933
Which $n$ can be expressed as $x^2 − y^2$?
116901
Monotonicity of $\frac{n}{\sqrt[n]{(n!)}}$
102738
Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.