A chain of triplets

Calculus Level 4

\[S=\dfrac { 1 }{ 1\cdot 2\cdot 3 } +\dfrac { 1 }{ 3\cdot 4\cdot 5 } +\dfrac { 1 }{ 5\cdot 6\cdot 7 } +\dfrac { 1 }{ 7\cdot 8\cdot 9 } +\frac { 1 }{ 9\cdot 10\cdot 11 } +\cdots \]

If \(S\) can be expressed in the form \(\ln { A } -\frac { 1 }{ A }\) with \(A\) being a positive, prime integer, find \(A\).


This problem is original.
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