P2188
If $x \in \mathbb{R}^n$, then
\begin{equation}
\begin{split}
\Big( \sum_{n = 1}^N f_n \Big) (- x) & = \sum_{n = 1}^N f_n(- x) \\
& = \sum_{n = 1}^N - f_n(x) = - \sum_{n = 1}^N f_n(x) = - \Big( \sum_{n = 1}^N f_n \Big) (x)
\end{split}
\end{equation}
$\square$
