# Determine whether the geometric series is convergent or divergent. If it is conv

nicekikah 2021-11-03 Answered
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. 3-4+16/3-64/9+........

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## Expert Answer

Faiza Fuller
Answered 2021-11-04 Author has 18760 answers
The given question already states that this is a geometric series.
A geometric series is convergent if and only if its common ratio r satisfies the following inequality
|r|
In the given problem, we have
$$\displaystyle{r}={\frac{{{a}_{{{2}}}}}{{{a}_{{{1}}}}}}={\frac{{-{4}}}{{{3}}}}$$
Since the absolute value of the common ratio is $$\displaystyle{\frac{{{4}}}{{{3}}}}\approx{1.33}$$, which is not less than 1, the given geometric series is divergent.
Results:
divergent because the common ratio is not less than 1.

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