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**1. Homework Statement**

Let (s_n) and (t_n) be bounded sequences of nonnegative numbers. Prove that limsup(s_n*t_n) <= (limsup(s_n))*(limsup(t_n)).

**2. Homework Equations**

**3. The Attempt at a Solution**

I know that (s_n) and (t_n) have convergent subsequences, but that's about it. Where could I go from here? Thanks!