Why is $\frac{2^{2n}}{2n} \leq {2n \choose n}$?
94291
$\frac{2^{2n}}{2n} \le {2n \choose n}$?
93994
Distribution of $\sum_{j=1}^n\ln\left(\frac{X_{(j)}}{X_{(1)}}\right)$ when $X_i$'s are i.i.d Pareto variables
136274
$n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
73418
Show that $\frac{(2n)!!}{(2n+1)!!}$ converges.
43226
Intuition behind logarithm inequality: $1 - \frac1x \leq \log x \leq x-1$
121880
How to show that $|D_{2n}| = 2n$ via the presentation?
27969
Why does $\frac{1}{x} < 4$ have two answers?
89186
Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
39504
Why does $ \frac{2x}{2+x}$ provide a particularly tight lower bound for $\ln(1+x)$ for small positive values of $x$?
132732
Estimate of n factorial: $n^{\frac{n}{2}} \le n! \le \left(\frac{n+1}{2}\right)^{n}$
1125
Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
26011
To show that $2$ | $x^{2n} - x^n$, $n \in \mathbb{Z^+}$ is the following adequate?
97805
$n+1$ is a divisor of $\binom{2n} {n}$
110264
Why are there $\frac{(2n)!}{2^nn!}$ ways to break $2n$ people into partnerships?
17638
Sum with binomial coefficients: $\sum_{k=0}^{n}{2n\choose 2k}$
35611
How can I show that $n! \leqslant \left(\frac{n+1}{2}\right)^n$?
97684
Show $\frac{(2n)!}{n!\cdot 2^n}$ is an integer for $n$ greater than or equal to $0$