What number comes next in the series? 5/6, 1/3, 1/2, 1/2, 2/8, 1/4, 5/6, 1/6,…

Concept: This series is built from groups of three fractions. Within each triplet, the first fraction equals the sum of the other two fractions in that triplet (first = second + third).

1. Triplet (5/6, 1/3, 1/2): 1/3 + 1/2 = 2/6 + 3/6 = 5/6, which matches the first term.

2. Triplet (1/2, 2/8, 1/4): 2/8 = 1/4, so 2/8 + 1/4 = 1/4 + 1/4 = 1/2, which matches the first term.

3. Triplet (5/6, 1/6, 2/3): 1/6 + 2/3 = 1/6 + 4/6 = 5/6, which matches the first term.

4. Triplet (1/2, 1/3, ?): the missing term x must satisfy 1/2 = 1/3 + x, so x = 1/2 - 1/3 = 3/6 - 2/6 = 1/6.

Cross-check: substituting x = 1/6 back gives 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2, which equals the first term, confirming the pattern holds.

So the missing number is 1/6.