\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}