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authormzuenni <michi.zuendorf@gmail.com>2024-09-08 22:16:36 +0200
committermzuenni <michi.zuendorf@gmail.com>2024-09-08 22:16:36 +0200
commit45d95c45013bf4ff73570c94c58b7f0212ccdf26 (patch)
treee47f9b16f44acef5f2517655fe2a16f8108f5af1 /content/math/tables/series.tex
parentdf963645ca0c5d0bed4fb9c02e93233dcfd53dae (diff)
moved stuff
Diffstat (limited to 'content/math/tables/series.tex')
-rw-r--r--content/math/tables/series.tex32
1 files changed, 16 insertions, 16 deletions
diff --git a/content/math/tables/series.tex b/content/math/tables/series.tex
index 3042781..9618c2b 100644
--- a/content/math/tables/series.tex
+++ b/content/math/tables/series.tex
@@ -1,33 +1,33 @@
-\begin{tabularx}{\linewidth}{|XIXIXIX|}
- \hline
- \multicolumn{4}{|c|}{Reihen} \\
+\begin{expandtable}
+\begin{tabularx}{\linewidth}{|XIXIX|}
\hline
$\sum\limits_{i = 1}^n i = \frac{n(n+1)}{2}$ &
$\sum\limits_{i = 1}^n i^2 = \frac{n(n + 1)(2n + 1)}{6}$ &
- $\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ &
- $H_n = \sum\limits_{i = 1}^n \frac{1}{i}$ \\
+ $\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ \\
\grayhline
- $\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \quad c \neq 1$ &
- $\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \quad \vert c \vert < 1$ &
- $\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \quad \vert c \vert < 1$ &
- $\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \quad \vert c \vert < 1$ \\
+ $\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \hfill c \neq 1$ &
+ $\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \hfill \vert c \vert < 1$ &
+ $\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \hfill \vert c \vert < 1$ \\
\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|}{
+ $\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \hfill \vert c \vert < 1$ \\
+ \grayhline
+
+ \multicolumn{2}{|lI}{
$\sum\limits_{i = 1}^n iH_i = \frac{n(n + 1)}{2}H_n - \frac{n(n - 1)}{4}$
- } \\
+ } &
+ $H_n = \sum\limits_{i = 1}^n \frac{1}{i}$ \\
\grayhline
\multicolumn{2}{|lI}{
- $\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$
- } &
- \multicolumn{2}{l|}{
$\sum\limits_{i = 1}^n \binom{i}{m}H_i =
\binom{n + 1}{m + 1} \left(H_{n + 1} - \frac{1}{m + 1}\right)$
- } \\
+ } &
+ $\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$ \\
\hline
\end{tabularx}
+\end{expandtable}