Answer:
The progression is Option A. convergent.
Step-by-step explanation:
The given series is( [tex]-\frac{8}{5}+\frac{32}{25}-\frac{128}{125}+......[/tex])
=[tex](-\frac{8}{5})(1-\frac{4}{5}+(\frac{4}{5})^{2}-.....)[/tex]
Now we can write this series as [tex]\sum_{n=0}^{n=\oe}(-\frac{8}{5})(-\frac{4}{5})^{n}[/tex]
In this expression common ration is 4/5= 0.8
As we know that in geometric progression if common factor is less than one then the progression converges.
Therefore we can say that this progression is convergent.
