To solve this problem, we need to find the sum of the given fractions:

1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96

First, we need to find a common denominator for all the fractions. The least common multiple (LCM) of the denominators 3, 6, 12, 24, 48, and 96 is 96.

Now, we can rewrite each fraction with the common denominator of 96:

(32/96) + (16/96) + (8/96) + (4/96) + (2/96) + (1/96)

Adding the numerators together, we get:

(32 + 16 + 8 + 4 + 2 + 1)/96

Simplifying the numerator, we have:

63/96

To simplify this fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 3:

(63/3)/(96/3) = 21/32

Therefore, the sum of the fractions 1/3 + 1/6 + 1/12 + 1/24 + 1/48 + 1/96 is equal to 21/32.