Question

6 (Picture) CONVERGENT AND DIVERGENT SERIES PLEASE HELP!!

Answer 1

Answer:

The progression is Option A. convergent.

Step-by-step explanation:

The given series is( $-\frac{8}{5}+\frac{32}{25}-\frac{128}{125}+......$)

=$(-\frac{8}{5})(1-\frac{4}{5}+(\frac{4}{5})^{2}-.....)$

Now we can write this series as $\sum_{n=0}^{n=\oe}(-\frac{8}{5})(-\frac{4}{5})^{n}$

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.