Observe the Sequence Below :

\(S= 1 - \frac{1}{3}+ \frac{1}{2}+ \frac{1}{9}+ \frac{1}{4}- \frac{1}{27}+ \frac{1}{8}+ \frac{1}{81}+ \frac{1}{16}- \frac{1}{243} + \cdot \cdot \cdot \cdot \cdot \cdot \cdot \)

What Is the Value of \(S\) ?

- \(S\) Can Be Written as \(\frac{a}{b}\) Where \(a\) and \(b\) are coprime positive integers.

Find \(a+b\)

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