Let $f$ be the function defined by $$f(x) = \sum_{n=1}^{+\infty} \left(\frac{1}{n+x} - \frac{1}{n}\right)$$ Determine $\mathcal{D}_{f}$, the domain of definition of $f$.
Let $f$ be the function defined by
$$f(x) = \sum_{n=1}^{+\infty} \left(\frac{1}{n+x} - \frac{1}{n}\right)$$
Determine $\mathcal{D}_{f}$, the domain of definition of $f$.