Final answer:
The series 3/2 + 9/8 + 27/32 + ... is a divergent geometric series with a common ratio greater than 1.
Step-by-step explanation:
The given series 3/2 + 9/8 + 27/32 + ... is a geometric series with a common ratio of (9/8).
To determine whether the series converges or diverges, we need to check if the absolute value of the common ratio is less than 1.
In this case, |9/8| = 9/8 which is greater than 1.
Since the absolute value of the common ratio is greater than 1, the series diverges.