What is the sum of the first 12 terms of the geometric series below
1/2+2+8+32+...
To find the sum of a geometric series, we use the formula
S = a * (1 - r^n) / (1 - r),
where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.
In the given series, the first term is 1/2 and the common ratio is 4 (each term is 4 times the previous term).
Using the formula, we can find the sum of the first 12 terms:
S = (1/2) * (1 - 4^12) / (1 - 4)
= (1/2) * (-16777215) / (-3)
= (1/2) * 5592405
= 2796202.5
Therefore, the sum of the first 12 terms of the series 1/2 + 2 + 8 + 32 + ... is 2,796,202.5.