For $x \in \mathbb{R} \backslash \mathbb{Z}$, justify that the series defining $g(x)$ is convergent, where $$g(x) = \frac{1}{x} + \sum_{n=1}^{+\infty} \left(\frac{1}{x+n} + \frac{1}{x-n}\right)$$
For $x \in \mathbb{R} \backslash \mathbb{Z}$, justify that the series defining $g(x)$ is convergent, where
$$g(x) = \frac{1}{x} + \sum_{n=1}^{+\infty} \left(\frac{1}{x+n} + \frac{1}{x-n}\right)$$