\[\large{S = 1 + \dfrac{1}{3} - \dfrac{1}{5} - \dfrac{1}{7} + \dfrac{1}{9} + \dfrac{1}{11} - \dfrac{1}{13} - \dfrac{1}{15} + \ldots}\]

If \(S\) can be expressed as \(\dfrac{\pi^A}{\sqrt{B}}\) for positive integers \(A,B\), submit the value of \(A+B\) as your answer.

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