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authorGloria Mundi <gloria@gloria-mundi.eu>2024-11-16 01:24:14 +0100
committerGloria Mundi <gloria@gloria-mundi.eu>2024-11-16 01:24:14 +0100
commit98567ec798aa8ca2cfbcb85c774dd470f30e30d4 (patch)
tree5113d5cc24d1ad5f93810b6442ce584a36950dc8 /math/tables/series.tex
parentad3856a6b766087df0036de0b556f4700a6498c9 (diff)
parent8d11c6c8213f46f0fa19826917c255edd5d43cb1 (diff)
mzuenni tests
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-\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}