Arithmetic-Geometric Series

Algebra Level 2

What is the value of S if: S=12+24+38+416+532+664+S=\frac { 1 }{ 2 } +\frac { 2 }{ 4 } +\frac { 3 }{ 8 } +\frac { 4 }{ 16 } +\frac { 5 }{ 32 } +\frac { 6 }{ 64 } +\dots

or S=n=1n2nS=\sum _{ n=1 }^{ \infty }{ \frac { n }{ { 2 }^{ n } } }

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