# Limited trigonometry

Calculus Level 5

$\large \sum_{r=1}^\infty \left[ \frac1{2^r} \tan\left( \frac{\pi /4}{2^r} \right) \right ]$

If the series above equals to $$A\pi^B + C$$ for integers $$A,B$$ and $$C$$, find the value of $$A\times B\times C$$.

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