# Infinite Summation + Infinite Products

Calculus Level 5

$\large\displaystyle\sum_{n=1}^{\infty}\prod_{k=n+1}^{\infty}\left(1-\left(\dfrac{n}k\right)^2\right)$ Let $$S$$ denote the value of series above. If $$S=\dfrac{A}{B}+\dfrac{C\pi}{D\sqrt{B}}$$ where $$A,B,C$$ and $$D$$ are coprime positive integers. Find the value of $$A+B+C+D$$.

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