8. In this question you must show detailed reasoning.
It is given that the geometric series
$$1 + \frac { 5 } { 3 x - 4 } + \left( \frac { 5 } { 3 x - 4 } \right) ^ { 2 } + \left( \frac { 5 } { 3 x - 4 } \right) ^ { 3 } + \ldots$$
is convergent.
- Find the set of possible values of \(x\), giving your answer in set notation.
- Given that the sum to infinity of the series is \(\frac { 2 } { 3 }\), find the value of \(x\).
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