Prove that $(n!)^2$ is greater than $n^n$ for all values of n greater than 2.
2554
Show that if $n>2$, then $(n!)^2>n^n$.
145891
Prove that $n! > \sqrt{n^n}, n \geq 3$
30783
Prove inequality $n<3^n$ using mathematical induction
31535
Solving an inequality : $n \geq 3$ , $n^{n} \lt (n!)^{2}$.
150156
Proving that $S_n$ has order $n!$
135614
Show that $2^n > n^2$ whenever n>4.
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
6223
Problem regarding radius of convergence of $\sum n!x^{n^2}$.
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
8034
Can $n!$ be a perfect square when $n$ is an integer greater than $1$?
88144
Induction Proof $n! < n^n$
62177
Prove that: $2^n < n!$ Using Induction
70386
Proof by induction: $2^n > n^2$ for all integer $n$ greater than $4$
88838
How can I prove this inequality for $n\geq 2$?
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$