Question

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

Answer 1

The progression is Option A. convergent.

Explanation:

The given series is(
`-(8)/(5)+(32)/(25)-(128)/(125)+......`)

=
`(-(8)/(5))(1-(4)/(5)+((4)/(5))^(2)-.....)`

Now we can write this series as
`\sum_(n=0)^(n=\oe)(-(8)/(5))(-(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.