# Arithmetic - Geometric Series Duality

Algebra Level 3

$\large \sum _{ n=1 }^{ \infty }{ \frac { n }{ { 3 }^{ n } } } =\frac { 1 }{ 3 } +\frac { 2 }{ 9 } +\frac { 3 }{ 27 } +\frac { 4 }{ 81 } +\cdots$

If the sum of the series above is in the form of $\dfrac ab$, where $a$ and $b$ are coprime positive integers, compute $a\times b$.

If you think the series diverges, enter the answer as -1.

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