\begin{expandtable}
\begin{tabularx}{\linewidth}{|C|}
	\hline
	$\frac{n!}{k!(n - k)!} \hfill=\hfill
	\binom{n}{k} \hfill=\hfill
	\binom{n}{n - k} \hfill=\hfill
	\frac{n}{k}\binom{n - 1}{k - 1} \hfill=\hfill
	\frac{n-k+1}{k}\binom{n}{k - 1} \hfill=\hfill
	\frac{k+1}{n-k}\binom{n}{k + 1} \hfill=\hfill$\\
	
	$\binom{n - 1}{k - 1} + \binom{n - 1}{k} \hfill=\hfill
	\binom{n + 1}{k + 1} - \binom{n}{k + 1} \hfill=\hfill
	(-1)^k \binom{k - n - 1}{k} \hfill\approx\hfill
	2^{n} \cdot \frac{2}{\sqrt{2\pi n}}\cdot\exp\left(-\frac{2(x - \frac{n}{2})^2}{n}\right)$\\
	\grayhline
	
	$\sum\limits_{k = 0}^n \binom{n}{k} = 2^n\hfill
	\sum\limits_{k = 0}^n \binom{k}{m} = \binom{n + 1}{m + 1}\hfill
	\sum\limits_{i = 0}^n \binom{n}{i}^2 = \binom{2n}{n}\hfill
	\sum\limits_{k = 0}^n\binom{r + k}{k} = \binom{r + n + 1}{n}$\\
	
	$\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n - k}{m - k}\hfill
	\sum\limits_{k = 0}^n \binom{r}{k}\binom{s}{n - k} = \binom{r + s}{n}\hfill
	\sum\limits_{i = 1}^n \binom{n}{i} \mathit{Fib}_i = \mathit{Fib}_{2n}$\\
	\hline
\end{tabularx}
\end{expandtable}