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**1. Homework Statement**

Show that limsup(s_n + t_n) <= limsup(s_n) + limsup(t_n) for bounded sequences (s_n) and (t_n).

**2. Homework Equations**

**3. The Attempt at a Solution**

My book gives a hint that says to first show that sup{s_n + t_n : n > N} <= sup{s_n : n > N} + sup{t_n : n > N}. I'm not really even sure how to do that. Any ideas? Thanks!