Calculate the sum of the given geometric series: ∑6n=1 20(1/2)^n−1 (1 point)
The sum of a geometric series can be calculated by the formula:
Sum = a(1 - r^n) / (1 - r)
where:
a = first term = 20(1/2)^1 = 10
r = common ratio = 1/2
n = number of terms = 6
Plugging the values into the formula:
Sum = 10(1 - (1/2)^6) / (1 - 1/2)
Sum = 10(1 - 1/64) / (1/2)
Sum = 10(63/64) / (1/2)
Sum = 630 / 32
Sum = 19.6875
Therefore, the sum of the given geometric series is 19.6875.