Factorial over Superfactorial!

S=11!+1×21!×2!+1×2×31!×2!×3!+S=\frac { 1 }{ 1! } +\frac { 1\times 2 }{ 1!\times 2! } +\frac { 1\times 2\times 3 }{ 1!\times 2!\times 3! } +\dots

S0=11!+11!×2!+11!×2!×3!+{ S }_{ 0 }=\frac { 1 }{ 1! } +\frac { 1 }{ 1!\times 2! } +\frac { 1 }{ 1!\times 2!\times 3! } +\dots

If SS0=AeBS-{ S }_{ 0 }=A{ e }^{ B } for integers A and B, find A+BA+B


Write 0.50.5 if SS diverges and S0{ S }_{ 0 } converges.

Write 1.51.5 if SS converges and S0{ S }_{ 0 } diverges.

Write 2.52.5 if SS and S0{ S }_{ 0 } diverge.

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