Final answer:
The series ∑₂⁻∞ 1/4n is a convergent geometric series because the common ratio 1/4 is less than 1. By applying the geometric series sum formula, it's shown that the series sums to a finite number.
Step-by-step explanation:
To determine whether the series ∑₂⁻∞ 1/4n is convergent or divergent, we can use the geometric series test. A geometric series of the form ∑rn is convergent if the common ratio |r| is less than 1; otherwise, it is divergent. In this case, r equals 1/4, which is less than 1, indicating that the series converges. Applying the formula for the sum of a convergent geometric series, S = a/(1 - r), where a is the first term and r is the common ratio, we find that the sum converges to a finite number.