Taylor y arc tan = \(\tan^{-1}\)

Calculus Level 4

\[\displaystyle \sum_{n = 1}^\infty \frac{(-1)^n}{4^n(2n + 1)}\]The sum above can be written as \[S=A\arctan \left(\dfrac{1}{A}\right) - B\] where \(A\) and \(B\) are coprime positive integers. Find \(10A + B\).

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