Convergent is not constant

1. A.if $liminf_{n}\to\infty a_{n} = limsup_{n}\to\infty a_{n}$, then $(a_{n})$ is convergent
2. B.if inf{$a_{n}$ | n ≥ 1} $= limsup_{n}\to\infty a_{n}$, then $(a_{n})$ is convergent
3. C.if sup{$a_{n}$ | n ≥ 1} $= liminf_{n}\to\infty a_{n}$, then $(a_{n})$ is constant✓ Correct
4. D.if sup{$a_{n}$ | n ≥ 1} = inf{$a_{n}$ | n ≥ 1}, then $(a_{n})$ is constant

The trap it tests

Reasoning with a limit before establishing there is one. limsup is not lim.