Given that
k=∞ 1 A*B-C*D
Σ ------------------ = -------
k=0 (3k+1)(3k+2)(3k+3) E
where A, B, C, D and E are, in some order, the number π (pi), the square root of an integer, the natural logarithm of an integer, and two integers, find their values.
pi*sqrt(3) - 3*ln(3)
S = -----------------------------
12