Question

Determine whether the series 3/2+9/8+27/32+ ... is convergent or divergent.

a.
convergent
b.
divergent

Answer 1

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.