Tinkering With The \(\zeta\) Function

Calculus Level 5

\[\large \sum_{n=1}^{\infty} \left(\dfrac{\zeta(2n)}{n} - \dfrac{1}{2n} - \dfrac{1}{2n+1} \right) \]

Find the value of the closed form of the above series.

Give your answer to 1 decimal place.

\[\] Notation: \(\zeta(\cdot) \) denotes the Riemann zeta function.

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