<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">Dokažte, že
$$\lim_{n\to \infty} \sqrt[n] { {a^n+b^n} }= \max\{a,b\}$$
pro $a,b$ nezáporná; podobně dokažte, že
$$\lim_{n \to \infty} \sqrt[n] { {a_1^n+\dots+a^n_k}} =
\max_{i=1,\dots,k}a_i$$
pro $a_i \ge 0$.
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