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Prove this statement about riemann zeta function

Source: 2009 Jozsef Wildt International Mathematical Competition

April 26, 2020

functionRiemann Zeta Function

Problem Statement

\zeta

denote the Riemann Zeta Function, and

s>1

then

\sum \limits_{k=1}^{\infty} \frac{1}{1+k^s}\geq \frac{\zeta (s)}{1+\zeta (s)}