I am trying to come up with different examples of the property that
$\limsup_{n\to\infty} (s_n + t_n) \leq \limsup_{n\to \infty} s_n+\limsup_{n\to \infty} t_n$
So I thought of
$s_n = \left \{-3,1,-1,1,-1,1,-1,...\right \}$ and $t_n = \left \{0,-1,1,-1,1,-1,1,...\right \}$
So $(s_n + t_n) = \left \{-3,0,0,0,0,0,... \right \}$ and $\limsup_{n\to\infty} (s_n + t_n)= 0$ and $\limsup_{n\to\infty} s_n = 1$ and $\limsup_{n\to\infty} t_n = 1$
Is this correct?