# 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 $$A$$.

×