We consider the power series in the real variable $x$ given by $\sum_{k \in \mathbb{N}^{*}} (-1)^{k} \zeta(k+1) x^{k}$. Determine the radius of convergence $R$ of this power series. Is there convergence at $x = \pm R$?
We consider the power series in the real variable $x$ given by $\sum_{k \in \mathbb{N}^{*}} (-1)^{k} \zeta(k+1) x^{k}$.
Determine the radius of convergence $R$ of this power series. Is there convergence at $x = \pm R$?