Final answer:
The sum of the first 12 terms of the series 1 + 2 + 4 + 8 + ... is 4095.
Step-by-step explanation:
The given series 1 + 2 + 4 + 8 + ... is a geometric series with a common ratio of 2. To find the sum of the first 12 terms, 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. Plugging in the values a = 1, r = 2, and n = 12, we get:
S = 1*(1 - 2^12)/(1 - 2) = 1*(-4095)/(-1) = 4095.