what is the sum of the first 12 terms of the geometric series below?
1/2 + 2 + 8 +32 +...
To find the sum of the first 12 terms of the geometric series, we can use the formula for the sum of a geometric series:
S = a * (1 - r^n) / (1 - r)
In this case, the first term (a) is 1/2 and the common ratio (r) is 2.
The number of terms (n) is 12.
Plugging these values into the formula:
S = (1/2) * (1 - 2^12) / (1 - 2)
S = (1/2) * (-2047) / (-1)
S = 1023
So, the sum of the first 12 terms of the geometric series is 1023.