\begin{expandtable}
\begin{tabularx}{\linewidth}{|XIXIX|}
	\hline
	$\sum\limits_{i = 1}^n i = \frac{n(n+1)}{2}$ &
	$\sum\limits_{i = 1}^n i^2 = \frac{n(n + 1)(2n + 1)}{6}$ &
	$\sum\limits_{i = 1}^n i^3 = \frac{n^2 (n + 1)^2}{4}$ \\
	\grayhline
	
	$\sum\limits_{i = 0}^n c^i = \frac{c^{n + 1} - 1}{c - 1} \hfill c \neq 1$ &	
	$\sum\limits_{i = 0}^\infty c^i = \frac{1}{1 - c} \hfill \vert c \vert < 1$ &
	$\sum\limits_{i = 1}^\infty c^i = \frac{c}{1 - c} \hfill \vert c \vert < 1$ \\
	\grayhline
		
	\multicolumn{2}{|lI}{
		$\sum\limits_{i = 0}^n ic^i = \frac{nc^{n + 2} - (n + 1)c^{n + 1} + c}{(c - 1)^2} \quad c \neq 1$
	} &	
	$\sum\limits_{i = 0}^\infty ic^i = \frac{c}{(1 - c)^2} \hfill \vert c \vert < 1$ \\
	\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}{
		$\sum\limits_{i = 1}^n \binom{i}{m}H_i =
		\binom{n + 1}{m + 1} \left(H_{n + 1} - \frac{1}{m  + 1}\right)$
	} &
	$\sum\limits_{i = 1}^n H_i = (n + 1)H_n - n$ \\
	\hline
\end{tabularx}
\end{expandtable}
