Prove, formally that: $\log_2 n! \ge n$ , for all integers $n>3$.
8609
Prove by induction that $n!>2^n$
98946
Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
13330
Inductive Proof that $k!<k^k$, for $k\geq 2$.
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
16798
Prove the inequality $n! \geq 2^n$ by induction
108504
Prove that for all non-negative integers $m,n$, $\frac{(2m)!(2n)!}{m!n!(m + n)!}$ is an integer.
146546
Proving for all integer $n \ge 2$, $\sqrt n < \frac{1}{\sqrt 1} + \frac{1}{\sqrt 2}+\frac{1}{\sqrt 3}+\cdots+\frac{1}{\sqrt n}$
2554
Show that if $n>2$, then $(n!)^2>n^n$.
149216
Give a combinatorial proof to show the following for all integers $n \geq 2$.
105985
Prove that all even integers $n \neq 2^k$ are expressible as a sum of consecutive positive integers
20691
prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer
122828
Proof that TREE(n) where n >= 3 is finite?
4750
Show that for any positive integer n, $(3n)!/(3!)^n$ is an integer.
45914
Proving that $n!≤((n+1)/2)^n$ by induction
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
150156
Proving that $S_n$ has order $n!$
90789
Use induction to prove that that $8^{n} | (4n)!$ for all positive integers $n$