Final answer:
The series 1, 1/16, 1/81, 1/256, 1/625, ... is convergent.
Step-by-step explanation:
To determine whether the series 1, 1/16, 1/81, 1/256, 1/625, ... is convergent or divergent, we need to examine the behavior of the terms as we go further in the series.
The given series is a geometric series with a common ratio of 1/4. In a geometric series, if the absolute value of the common ratio is less than 1, the series converges. Otherwise, it diverges.
Since the absolute value of the common ratio 1/4 is less than 1, the series is convergent.