For every $s > 1$, let $\zeta(s) = \sum_{n=1}^{+\infty} \frac{1}{n^s}$. Determine $C(s)$ such that $$\forall s \in ]1, +\infty[, \quad \sum_{k=1}^{+\infty} \frac{1}{(2k-1)^s} = C(s) \zeta(s).$$
For every $s > 1$, let $\zeta(s) = \sum_{n=1}^{+\infty} \frac{1}{n^s}$. Determine $C(s)$ such that
$$\forall s \in ]1, +\infty[, \quad \sum_{k=1}^{+\infty} \frac{1}{(2k-1)^s} = C(s) \zeta(s).$$