Formal way to proof that $k! > (k/2)^{(k/2)}$ for any $k \in \{1,2,3,4...\}$
87813
How to show that for all k, $k! \ge (k/2)^{k/2}$
126574
Proving $\prod_k \sin \pi k / n = n / 2^{n-1}$
67650
Short and intuitive proof that $\left(\frac{n}{k}\right)^k \leq \binom{n}{k}$
139503
How to prove $|a+b|^k \leq 2^{k-1} (|a|^k+|b|^k)$?
96903
How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $?
153100
A counterexample to "$k\mid n$ if and only if $k\mid n^2$"
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
155005
How to show $\sum_{k=n}^\infty{\frac{1}{k!}} \leq \frac{2}{n!}$
136737
Proof by Induction for inequality, $\sum_{k=1}^nk^{-2}\lt2-(1/n)$
139229
How to prove by arithmetical means that $\sum\limits_{k=1}^\infty \frac{((k-1)!)^2}{(2k)!} =\frac{1}{3}\sum\limits_{k=1}^{\infty}\frac{1}{k^{2}}$
7843
Show that order of $a^k$
44864
Prove, formally that: $\log_2 n! \ge n$ , for all integers $n>3$.
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?
153123
Proving by induction $4^n  0$
152104
How do I prove that $ij = k?$
8609
Prove by induction that $n!>2^n$