what is the sum of the first 12 terms of the geometric series below?
1/2+2+8+32...
4,095/512
20,735/22
2,097,152
5,592,405/2
To find the sum of the first 12 terms of the geometric series, we 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.
Given the series 1/2 + 2 + 8 + 32..., we can see that the first term (a) is 1/2 and the common ratio (r) is 4.
Plugging in these values into the formula:
S = (1/2)(1 - 4^12) / (1 - 4)
= (1/2)(1 - 16,777,216) / (1 - 4)
= (1/2)(-16,777,215)/(-3)
= 8,388,607/3
Therefore, the sum of the first 12 terms of the geometric series is 8,388,607/3, which is approximately equal to 2,796,202.33.