what is the sum of the first 12 terms of the geometric series below?
1/2 + 2 + 8 + 32 +...
A. 4,095/512
B. 20,735/22
C. 2,097,152
or D. 5,592,405/2
Apologies for the confusion. From the given answer options, the closest approximation to the sum of the first 12 terms of the geometric series is B. 20,735/22.
To find the sum of the first 12 terms of the geometric series 1/2 + 2 + 8 + 32 +..., we can use the formula for the sum of a geometric series:
S = a(1 - r^n) / (1 - r),
where S is the sum, 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 1/2 and the common ratio (r) is 4. The number of terms (n) is 12.
Using the formula:
S = (1/2)(1 - 4^12) / (1 - 4)
= (1/2)(1 - 16,777,216) / (1 - 4)
= (1/2)(-16,777,215) / (-3)
= (8,388,607/2) / 3
= 8,388,607 / 6
= 1,398,101.17.
Since the sum is not an exact integer, none of the given answer options are correct.