Let $x_n$ and $y_n$ be bounded sequences of real numbers.
Show that:
$$ \lim \sup(x_n+y_n) \leq \lim \sup x_n+\lim \sup y_n $$
2026-03-30 07:07:27.1774854447
Prove bounded sequences of real numbers
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Hint
Obviously, $$\sup_{k\geq n}(x_k+y_k)\leq \sup_{k\geq n}x_k+\sup_{k\geq n}y_k.$$