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Diffstat (limited to 'math/tables/series.tex')
| -rw-r--r-- | math/tables/series.tex | 33 |
1 files changed, 0 insertions, 33 deletions
diff --git a/math/tables/series.tex b/math/tables/series.tex deleted file mode 100644 index 3042781..0000000 --- a/math/tables/series.tex +++ /dev/null @@ -1,33 +0,0 @@ -\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} |