Bounded sequences and lim inf Let $a_n$ and $b_n$ be bounded sequences. Prove that lim inf $a_n$ + lim inf $b_n \leq$ lim inf$(a_n + b_n)$
I have no idea where to begin.

Start by showing that for all $n$, $$\inf_{k\geq n}a_k+\inf_{k\geq n}b_k\leq\inf_{k\geq n}(a_k+b_k),$$ then take the limit as $n\to\infty$.
