Let $f(x) = \pi \operatorname{cotan}(\pi x)$, $g(x) = \frac{1}{x} + \sum_{n=1}^{+\infty}\left(\frac{1}{x+n} + \frac{1}{x-n}\right)$, and $D = f - g$. Show that the functions $g$ and $D$ are odd.
Let $f(x) = \pi \operatorname{cotan}(\pi x)$, $g(x) = \frac{1}{x} + \sum_{n=1}^{+\infty}\left(\frac{1}{x+n} + \frac{1}{x-n}\right)$, and $D = f - g$. Show that the functions $g$ and $D$ are odd.