# Not Geometric, Not Arithmetic...

Algebra Level 4

If the infinite series $${ S }_{ \infty } = \sum _{ n=0 }^{ \infty }{ \frac { 2n+1 }{ { 2 }^{ 2n+1 } } }$$ can be represented as $$\frac { A }{ B }$$, where $$A$$ and $$B$$ are positive coprime integers, then evaluate $$A + B$$.

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