Could someone please check my work I don't think the first part is quite right

Let (S, ) and (tn) be bounded sequences. 1. Prove that lim sup (sn + tn) 0, 3N1 such that n > N1 which implies that S, N2 which implies that tn max {N1, N2} = Suttn max {N1, N2} + Sn _ k+ tn _ k