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

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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