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\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}
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