4: The sequence goes
a₀ = 1/2,
a₁ = 0,
a₂ = 3/4,
a₃ = 2/5.

When n tends to infinity, the alternating part and the "+2" can be ignored (see intuitive calculation) and the sequence looks like n/n = 1.

Next hint - boundedness
Next hint - monotonicity
Answer