16. A geometric series is \(a + a r + a r ^ { 2 } + \ldots\)
- Prove that the sum of the first \(n\) terms of this series is given by
$$S _ { n } = \frac { a \left( 1 - r ^ { n } \right) } { 1 - r }$$
The second and fourth terms of the series are 3 and 1.08 respectively.
Given that all terms in the series are positive, find - the value of \(r\) and the value of \(a\),
- the sum to infinity of the series.