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S=11⋅2⋅3+12⋅3⋅4+13⋅4⋅5+14⋅5⋅6+15⋅6⋅7+⋯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 } +\cdotsS=1⋅2⋅31+2⋅3⋅41+3⋅4⋅51+4⋅5⋅61+5⋅6⋅71+⋯
If SSS can be expressed in the form 1A\frac { 1 }{ A }A1 with AAA being a positive, composite integer, find AAA.
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