A growth of triplets

Algebra Level 4

$S=\dfrac { 1 }{ 1\cdot 2\cdot 3 } +\dfrac { 1 }{ 2\cdot 3\cdot 4 } +\dfrac { 1 }{ 3\cdot 4\cdot 5 } +\dfrac { 1 }{ 4\cdot 5\cdot 6 } +\dfrac { 1 }{ 5\cdot 6\cdot 7 } +\cdots$

If $S$ can be expressed in the form $\frac { 1 }{ A }$ with $A$ being a positive, composite integer, find $A$ .