# 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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