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I have a sequence, called $A$. It's elements are $a_1 , a_2 , \ldots , a_n $ for example: $(5, 11, 2)$

Then how to prove, that this formula results the highest value in the series?

$$ \lim_{x \rightarrow \infty} \sqrt[x]{ \sum\limits_{i=1}^n a_i^x } = \max( a_1, \ldots, a_n ) $$

Iter Ator
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  • Writing \max instead of just max has three effects: (1) it causes "$\max$" not to be italicized; (2) it results in proper spacing in expressions like $a\max b$; (3) in a "displayed" rather than "inline" setting, it makes subscripts appear directly below the symbol, thus: $\displaystyle\max_{x\in S}f(x)$. It is standard usage. I also changed "..." to "\ldots", and that also affects spacing when TeX or LaTeX is used (as opposed to MathJax, which is what is used here). I edited accordingly. ${}\qquad{}$ – Michael Hardy Mar 13 '15 at 16:58

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hint: $$\text{max}(a_1,a_2,\cdots,a_n) \leq S \leq n^{\frac{1}{x}}\cdot\text{max}(a_1,a_2,\cdots,a_n)$$

DeepSea
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