Limita unui sir integral 1

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Cezar Lupu
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Limita unui sir integral 1

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Fie \( I_{n}=\int_0^1 (1-x^{n})^{n}dx \), \( n\in\mathbb{N} \)
Sa se calculeze \( \lim_{n\to\infty} I_{n} \).
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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