Let $x \in \mathcal{D}_{\zeta}$ and let $n \in \mathbb{N}$ such that $n \geqslant 2$. Show: $$\int_{n}^{n+1} \frac{\mathrm{~d}t}{t^{x}} \leqslant \frac{1}{n^{x}} \leqslant \int_{n-1}^{n} \frac{\mathrm{~d}t}{t^{x}}$$
Let $x \in \mathcal{D}_{\zeta}$ and let $n \in \mathbb{N}$ such that $n \geqslant 2$. Show:
$$\int_{n}^{n+1} \frac{\mathrm{~d}t}{t^{x}} \leqslant \frac{1}{n^{x}} \leqslant \int_{n-1}^{n} \frac{\mathrm{~d}t}{t^{x}}$$