# A series inspired by Satyajit

Calculus Level 5

$\large{S = \frac{2}{3\times 4}+\frac{2 \times 4}{3\times 5 \times 6}+\frac{2\times 4 \times 6}{3\times 5\times 7\times 8}+ \ldots}$

If $$S$$ can be expressed as $$\dfrac{\pi^{A}}{B}-\dfrac{C}{D}$$ where $$A,B,C,D$$ are positive integers with $$C$$ and $$D$$ as coprime positive integers, evaluate $$A\times B\times C\times D$$.

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