To find the sum of the given series, we can observe that each term is in the form 1/(2^n * 3), where n starts from 1 and increases by 1 for each subsequent term.

So, the series can be written as:

1/6 + 1/12 + 1/24 + ... + 1/768 = Σ(1/(2^n * 3))

To find the sum, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where S is the sum, a is the first term, and r is the common ratio.

In this case, a = 1/6 and r = 1/2 * 1/3 = 1/6.

Plugging in these values, we get:

S = (1/6) / (1 - 1/6)
= (1/6) / (5/6)
= 1/5

Therefore, the sum of the series 1/6 + 1/12 + 1/24 + ... + 1/768 is 1/5.