400 Followers Problem - Reciprocal Summations 1

Calculus Level 5

S=1+131517+19+111113115+\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 SS can be expressed as πAB\dfrac{\pi^A}{\sqrt{B}} for positive integers A,BA,B, submit the value of A+BA+B as your answer.


Also try these:
400 Followers Problem - Reciprocal Summations #2
400 Followers Problem - Reciprocal Summations #3
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