Final answer:
The sum of the geometric series 4 ∑ 3(3/4)^i is calculated to be 525/64, which corresponds to option c in the provided choices.
Step-by-step explanation:
The sum of the geometric series 4 ∑ 3(3/4)i can be found using the formula for the sum of a finite geometric series which is Sn = a(1 - rn) / (1 - r), where 'a' is the first term, 'r' is the common ratio, and 'n' is the number of terms. In this case, the first term 'a' is 3, the common ratio 'r' is 3/4, and the series has 4 terms. Substituting the values into the formula gives us S4 = 3(1 - (3/4)4) / (1 - 3/4) = 3(1 - 81/256) / (1/4) = 3(175/256) / (1/4) = 3(175/256) * 4 = 2100/256, which simplifies to 525/64, which is option c).