To solve this sequence problem, let's analyze the pattern:

Sequence:

$\frac{1}{2}, \frac{2}{3}, \frac{5}{6}, \frac{1}{1}, \, ?$

1. Numerator Pattern:

   • The numerators are $1, 2, 5, 1$.
   • This appears to follow no strict arithmetic or geometric progression, but we notice it alternates back to 1.

2. Denominator Pattern:

   • The denominators are $2, 3, 6, 1$.
   • Observe: $2 \to 3 \to 6 \to 1$.
   • This sequence doesn't seem arithmetic but may involve alternation or resetting.

Conclusion:

The sequence seems cyclic in nature, where the pattern of numerators and denominators are repeated,