From 4557d41296204719d8f56bb3efadc38858e9f658 Mon Sep 17 00:00:00 2001
From: Paul Jungeblut <paul.jungeblut@gmail.com>
Date: Sun, 19 Nov 2017 22:41:30 +0100
Subject: Changing order of two maths tables to get back into the 25 pages.

---
 math/math.tex | 62 +++++++++++++++++++++++++++++------------------------------
 1 file changed, 31 insertions(+), 31 deletions(-)

(limited to 'math/math.tex')

diff --git a/math/math.tex b/math/math.tex
index 430d533..cc8d263 100644
--- a/math/math.tex
+++ b/math/math.tex
@@ -295,6 +295,37 @@ Anzahl der Teilmengen von $\mathbb{N}$, die sich zu $n$ aufaddieren mit maximale
 \end{tabular}
 \vspace{5mm}
 
+\begin{tabular}{l|l|l}
+	\toprule
+	\multicolumn{3}{c}{Reihen} \\
+	\midrule
+	$\sum\limits_{i = 1}^n i = \frac{n(n+1)}{2}$ &
+	$\sum\limits_{i = 1}^n i^2 = \frac{n(n + 1)(n + 2)}{6}$ & 
+	$\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ \\
+
+	$\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \quad c \neq 1$ &
+	$\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \quad \vert c \vert < 1$ &
+	$\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \quad \vert c \vert < 1$ \\
+
+	\multicolumn{2}{l|}{
+		$\sum\limits_{i = 0}^n ic^i = \frac{nc^{n + 2} - (n + 1)c^{n + 1} + c}{(c - 1)^2} \quad c \neq 1$
+	} &
+	$\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \quad \vert c \vert < 1$ \\
+
+	$H_n = \sum\limits_{i = 1}^n \frac{1}{i}$ &
+	\multicolumn{2}{l}{
+		$\sum\limits_{i = 1}^n iH_i = \frac{n(n + 1)}{2}H_n - \frac{n(n - 1)}{4}$
+	} \\
+
+	$\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$ &
+	\multicolumn{2}{l}{
+		$\sum\limits_{i = 1}^n \binom{i}{m}H_i =
+		\binom{n + 1}{m + 1} \left(H_{n + 1} - \frac{1}{m  + 1}\right)$
+	} \\
+	\bottomrule
+\end{tabular}
+\vspace{5mm}
+
 \begin{tabular}{c|cccc}
 	\toprule
 	\multicolumn{5}{c}{The Twelvefold Way (verteile $n$ Bälle auf $k$ Boxen)} \\
@@ -505,37 +536,6 @@ Anzahl der Teilmengen von $\mathbb{N}$, die sich zu $n$ aufaddieren mit maximale
 \end{tabular}
 \vspace{5mm}
 
-\begin{tabular}{l|l|l}
-	\toprule
-	\multicolumn{3}{c}{Reihen} \\
-	\midrule
-	$\sum\limits_{i = 1}^n i = \frac{n(n+1)}{2}$ &
-	$\sum\limits_{i = 1}^n i^2 = \frac{n(n + 1)(n + 2)}{6}$ & 
-	$\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ \\
-
-	$\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \quad c \neq 1$ &
-	$\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \quad \vert c \vert < 1$ &
-	$\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \quad \vert c \vert < 1$ \\
-
-	\multicolumn{2}{l|}{
-		$\sum\limits_{i = 0}^n ic^i = \frac{nc^{n + 2} - (n + 1)c^{n + 1} + c}{(c - 1)^2} \quad c \neq 1$
-	} &
-	$\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \quad \vert c \vert < 1$ \\
-
-	$H_n = \sum\limits_{i = 1}^n \frac{1}{i}$ &
-	\multicolumn{2}{l}{
-		$\sum\limits_{i = 1}^n iH_i = \frac{n(n + 1)}{2}H_n - \frac{n(n - 1)}{4}$
-	} \\
-
-	$\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$ &
-	\multicolumn{2}{l}{
-		$\sum\limits_{i = 1}^n \binom{i}{m}H_i =
-		\binom{n + 1}{m + 1} \left(H_{n + 1} - \frac{1}{m  + 1}\right)$
-	} \\
-	\bottomrule
-\end{tabular}
-\vspace{5mm}
-
 \begin{tabular}{ll}
 	\toprule
 	\multicolumn{2}{c}{Verschiedenes} \\
-- 
cgit v1.2.3

