A chain of triplets

Calculus Level 3

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

The sum \(S\) can be expressed in the form \(\ln { A } -\frac { 1 }{ A },\) where \(A\) is a prime number.