Could someone please check my work. I'm not sure it's quite right.

Let (Sn) and (tn) be bounded sequences. 1. Prove that lim sup (sn + tn) S lim sup s, + lim sup tn . Let lim sup sn = S and let lim sup tn = T. By Theorem 4.4.11, VE > 0, 3Ni such that n > N1 which implies that Sn N2 which implies that tn max {N1, N2} # Snt tn max {N1, N2} - snk +try. :