Final answer:
The series 12/5 + 48/25 + 192/125 + ... is a divergent geometric series with a common ratio of 4/5.
Therefore, the correct answer is: option b) divergent.
Step-by-step explanation:
To determine whether the series converges or diverges, we can use the comparison test.
Let's compare the given series with the convergent series 1 + (4/5) + (4/5)^2 + ...
The nth term of the given series is (12/5) * (4/5)^(n-1).
The nth term of the convergent series is (4/5)^(n-1).
By comparing the terms, we can see that every term of the given series is 3 times the corresponding term of the convergent series.
Since the terms of the convergent series decrease, and the given series is always larger, we can conclude that the given series diverges.
Therefore, the series 12/5 + 48/25 + 192/125 + ... is a divergent geometric series.