From 5ab8a5088b729a9953b8dff1b2a985dc8fb2098b Mon Sep 17 00:00:00 2001
From: mzuenni <michi.zuendorf@gmail.com>
Date: Mon, 27 Jun 2022 17:19:28 +0200
Subject: updated tcr

---
 math/tables/binom.tex | 28 ++++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)
 create mode 100644 math/tables/binom.tex

(limited to 'math/tables/binom.tex')

diff --git a/math/tables/binom.tex b/math/tables/binom.tex
new file mode 100644
index 0000000..878a6b0
--- /dev/null
+++ b/math/tables/binom.tex
@@ -0,0 +1,28 @@
+\begin{tabularx}{\linewidth}{|XXXX|}
+	\hline
+	\multicolumn{4}{|c|}{Binomialkoeffizienten} \\
+	\hline
+	\multicolumn{4}{|c|}{
+	$\frac{n!}{k!(n - k)!} \hfill=\hfill
+	\binom{n}{k} \hfill=\hfill
+	\binom{n}{n - k} \hfill=\hfill
+	\frac{n}{k}\binom{n - 1}{k - 1} \hfill=\hfill
+	\frac{n-k+1}{k}\binom{n}{k - 1} \hfill=\hfill
+	\binom{n - 1}{k} + \binom{n - 1}{k - 1} \hfill=\hfill
+	(-1)^k \binom{k - n - 1}{k} \hfill\approx\hfill
+	2^{n} \cdot \frac{2}{\sqrt{2\pi n}}\cdot\exp\left(-\frac{2(x - \frac{n}{2})^2}{n}\right)$
+	} \\
+	\grayhline
+	
+	$\sum\limits_{k = 0}^n \binom{n}{k} = 2^n$ &
+	$\sum\limits_{k = 0}^n \binom{k}{m} = \binom{n + 1}{m + 1}$ &
+	$\sum\limits_{i = 0}^n \binom{n}{i}^2 = \binom{2n}{n}$ &
+	$\sum\limits_{k = 0}^n\binom{r + k}{k} = \binom{r + n + 1}{n}$\\
+	
+	$\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n - k}{m - k}$ &
+	$\sum\limits_{k = 0}^n \binom{r}{k}\binom{s}{n - k} = \binom{r + s}{n}$ &
+	\multicolumn{2}{l|}{
+	$\sum\limits_{i = 1}^n \binom{n}{i} F_i = F_{2n} \quad F_n = n\text{-th Fib.}$
+	}\\
+	\hline
+\end{tabularx}
-- 
cgit v1.2.3

