diff options
| author | mzuenni <michi.zuendorf@gmail.com> | 2024-09-08 22:16:36 +0200 |
|---|---|---|
| committer | mzuenni <michi.zuendorf@gmail.com> | 2024-09-08 22:16:36 +0200 |
| commit | 45d95c45013bf4ff73570c94c58b7f0212ccdf26 (patch) | |
| tree | e47f9b16f44acef5f2517655fe2a16f8108f5af1 /content/math/tables/series.tex | |
| parent | df963645ca0c5d0bed4fb9c02e93233dcfd53dae (diff) | |
moved stuff
Diffstat (limited to 'content/math/tables/series.tex')
| -rw-r--r-- | content/math/tables/series.tex | 32 |
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} |
