Final answer:
The series 2/5, 4/25, 8/125, 16/625, 32/3125 is a convergent geometric series because the ratio between its consecutive terms is less than 1, resulting in a decreasing sequence of positive numbers.
Step-by-step explanation:
The given series is 2/5, 4/25, 8/125, 16/625, 32/3125, which appears to be a geometric series where each term is obtained by multiplying the previous term by a constant ratio. To determine if the series is convergent or divergent, we can apply the ratio test for convergence of infinite series. The ratio between consecutive terms is (2/5)/(4/25) = 25/40 = 5/8, and similarly for the other terms. Because this ratio is less than 1, the series is convergent.
The given series is always positive and steadily decreasing since each term is positive and is a fraction of the previous term. Hence, the answer to the query is that the series is convergent.