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Convergence of series, sequences and functions and different modes of convergence.
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Speed of convergence of $\zeta(2k)\to 1$?
From the definition of $\zeta(z):= \sum_{k=1}^\infty \tfrac{1}{k^z}$ for $\mathrm{Re}(z)>1$ it is obvious that $\zeta(2k)\downarrow 1$ as $k \rightarrow \infty$. I am interested in the "true" speed of …