convergenta uniforma a unei serii de functii

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Cezar Lupu
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convergenta uniforma a unei serii de functii

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Fie sirul de fucntii \( f_{n};[0,1]\to\mathbb{R} \) definit prin \( f_{n}(x)=x^{n}(1-x^{2n}) \). Sa se studieze convergenta simpla si uniforma a seriei
\( \sum_{n=0}^{\infty}(f_{n}(x))^{\alpha} \) unde \( \alpha>0 \) este dat.
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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