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Calculus Level 3

\[\frac { 1 }{ 3 } +\frac { 2 }{ 9 } +\frac { 3 }{ 27 } +\frac { 4 }{ 81 } +\frac { 5 }{ 729 } + \frac { 8 } { 2187} + \frac{ 7}{ 6561} + \ldots \]

i.e. Evaluate \[ \sum_{n=1}^{\infty} \left( \left(\dfrac{1}{3}\right)^n + \left(\dfrac{2}{9}\right)^n \right) = \dfrac {a}{b}\]

If \(a,b\) are co-prime integers, calculate \(ab\).


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