A Squared Riemann Zeta

Calculus Level 5

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

If the value of the series above is equal to \(\dfrac{\pi^A}{B} \), where \(A\) and \(B\) are integers, find \(A+B\).

Notations

  • \(\zeta(\cdot) \) denote the Riemann zeta function.

  • \(B_n\) denote the \(n^\text{th} \) Bernoulli number.

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