Final answer:
The sum of the infinite geometric series is 128.
Step-by-step explanation:
An infinite geometric series is a series in which each term after the first is found by multiplying the previous term by a constant ratio. The formula for the sum of an infinite geometric series is:
S = a / (1 - r)
Where 'a' is the first term and 'r' is the common ratio.
In the given series, the first term is 64 and the common ratio is 1/2. Plugging these values into the formula, we get:
S = 64 / (1 - 1/2) = 64 / (1/2) = 128
Therefore, the sum of the infinite geometric series is 128.