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**EinStone** A Dirichlet series is just a series $\displaystyle \sum_{n=1}^{\infty} \dfrac{a_n}{n^s}$, where $\displaystyle a_n$ is any sequence of complex numbers, and $\displaystyle s\in \mathbb{C}$. We consider the convergence of the series depending on s.

I need help with the proof of a corollary, stating that if $\displaystyle \sum_{n=1}^{\infty} \dfrac{a_n}{n^{s_0}}$ converges for some $\displaystyle s_0 \in \mathbb{C}$, then it converges absolutely for any $\displaystyle s_1 \in \mathbb{C}$ with $\displaystyle Re(s_1) > Re(s_0)+1$