O limita magnifica (Isaac Schoenberg)

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Cezar Lupu
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O limita magnifica (Isaac Schoenberg)

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Sa se arate ca \( \lim_{n\to\infty}\frac{1^n+2^n+\ldots +n^n}{n^n}=\frac{e}{e-1}. \)
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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