To determine if the given geometric series is convergent or divergent, we first need to identify the common ratio and the nature of the series.
A geometric series can be expressed in the form:
a + a * r + a * r^2 + …
where a is the first term and r is the common ratio between subsequent terms.
In this case, we first need to confirm if the series is indeed geometric by checking the ratio between consecutive terms:
- 8 / 10 = 0.8
- 64 / 8 = 8
- 512 / 64 = 8
The ratios differ, indicating this series does not have a constant ratio. This means the series is not geometric.
Since it is not a geometric series, we cannot apply the convergence criteria specific to geometric series.
Thus, we conclude that the series formed by the numbers 10, 8, 64, and 512 is neither convergent nor divergent in the context of a geometric series as it does not fit the definition of a geometric series.