Riemann zeta

Consider the function $\zeta$ defined by the series $$\zeta(z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{n^z}.$$

Convergence

Proposition: If $\mathrm{Re} \hspace{2pt} z > 1$, then the series defining $\zeta(z)$ converges.

Proof: █