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.

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.