# Factorial over Superfactorial!

$S=\frac { 1 }{ 1! } +\frac { 1\times 2 }{ 1!\times 2! } +\frac { 1\times 2\times 3 }{ 1!\times 2!\times 3! } +\dots$

${ S }_{ 0 }=\frac { 1 }{ 1! } +\frac { 1 }{ 1!\times 2! } +\frac { 1 }{ 1!\times 2!\times 3! } +\dots$

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

Write $0.5$ if $S$ diverges and ${ S }_{ 0 }$ converges.

Write $1.5$ if $S$ converges and ${ S }_{ 0 }$ diverges.

Write $2.5$ if $S$ and ${ S }_{ 0 }$ diverge.

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