Show $\left( n!\right)^2 > n^n$.
2554
Show that if $n>2$, then $(n!)^2>n^n$.
46661
A binomial inequality with factorial fractions: $\left(1+\frac{1}{n}\right)^n<\frac{1}{0!}+\frac{1}{1!}+\frac{1}{2!}+...+\frac{1}{n!}$
16798
Prove the inequality $n! \geq 2^n$ by induction
4750
Show that for any positive integer n, $(3n)!/(3!)^n$ is an integer.
97666
Prove $133\mid \left(11^{n+2}+12^{2n+1}\right)$
70386
Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
130093
Prove by Induction : $n < 2^n$
126889
Proof by induction: inequality $n! > n^3$ for $n > 5$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$
69673
Prove that $\left (\frac{a^2 + b^2 +c^2}{a+b+c} \right) ^ {(a+b+c)} > a^a b^b c^c$
35169
Finding the limit of $\left(\frac{n}{n+1}\right)^n$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
145423
prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
85731
Prove by induction that $n! > n^2$
83149
Factorial Inequality problem $\left(\frac n2\right)^n > n! > \left(\frac n3\right)^n$
2708
Inequality ${n \choose k} \leq \left(\frac{en}{ k}\right)^k$