((picture) convergent and divergent series

A

Step-by-step explanation:

A series is said to be convergent if |r| < 1. Where r is the common ratio of the series.

If |r| ≥ 1 then the geometric series diverges.

8/5 + 32/25 + 128/125 + ...

r = 128/125 ÷ 32/25 = 128/125×25/32 = 4/5

r = 32/25 ÷ 8/5 = 32/25 × 5/8 = 4/5

In the series is less than 1. So the series is convergent.

12r - 8 - 12

you have to combine like terms. below i have bolded the like terms:

12r - 8 - 12

together it combines to:

12r - 20

hope this !