# Inverse Trigonometric Series Product!

Geometry Level 5

$\large S_n = \prod_{k=1}^n \frac{\arcsin \left( \frac{9k+2}{\sqrt{27k^3 + 54k^2 + 36k + 8}} \right) }{\arctan \left( \frac{1}{\sqrt{3k+1}} \right)}$

Find the value of $$\ln(S_{2015})$$ correct to three places of decimal.

Bonus: Generalize for $$S_n, n \in \mathbb Z^+$$.

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