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/series.tex | 33 +++++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)
 create mode 100644 math/tables/series.tex

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

diff --git a/math/tables/series.tex b/math/tables/series.tex
new file mode 100644
index 0000000..13af68f
--- /dev/null
+++ b/math/tables/series.tex
@@ -0,0 +1,33 @@
+\begin{tabularx}{\linewidth}{|XIXIXIX|}
+	\hline
+	\multicolumn{4}{|c|}{Reihen} \\
+	\hline
+	$\sum\limits_{i = 1}^n i = \frac{n(n+1)}{2}$ &
+	$\sum\limits_{i = 1}^n i^2 = \frac{n(n + 1)(2n + 1)}{6}$ & 
+	$\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ &
+	$H_n = \sum\limits_{i = 1}^n \frac{1}{i}$ \\
+	\grayhline
+	
+	$\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \quad c \neq 1$ &	
+	$\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \quad \vert c \vert < 1$ &
+	$\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \quad \vert c \vert < 1$ &	
+	$\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \quad \vert c \vert < 1$ \\
+	\grayhline
+	
+	\multicolumn{2}{|lI}{
+		$\sum\limits_{i = 0}^n ic^i = \frac{nc^{n + 2} - (n + 1)c^{n + 1} + c}{(c - 1)^2} \quad c \neq 1$
+	} &	
+	\multicolumn{2}{l|}{
+		$\sum\limits_{i = 1}^n iH_i = \frac{n(n + 1)}{2}H_n - \frac{n(n - 1)}{4}$
+	} \\
+	\grayhline
+	
+	\multicolumn{2}{|lI}{
+		$\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$
+	} &
+	\multicolumn{2}{l|}{
+		$\sum\limits_{i = 1}^n \binom{i}{m}H_i =
+		\binom{n + 1}{m + 1} \left(H_{n + 1} - \frac{1}{m  + 1}\right)$
+	} \\
+	\hline
+\end{tabularx}
\ No newline at end of file
-- 
cgit v1.2.3

