# Staggered triplets

Calculus Level 4

$S=\dfrac { 1 }{ 1\cdot 3\cdot 5 } +\dfrac { 1 }{ 2\cdot 4\cdot 6 } +\dfrac { 1 }{ 3\cdot 5\cdot 7 } +\dfrac { 1 }{ 4\cdot 6\cdot 8 } +\dfrac { 1 }{ 5\cdot 7\cdot 9 } + \cdots$

If $S$ can be expressed in the form $\frac { A }{ { B }^{ C }D }$ with $A$, $B$, $C$, and $D$ being positive prime integers, find the value of $\dfrac { A+B+C+D }{ D }.$

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