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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.

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up vote 2 down vote accepted

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 $n\to\infty$.

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