Seria armonica cu sin

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Cezar Lupu
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Seria armonica cu sin

Post by Cezar Lupu »

Sa se studieaze convergenta seriei

\( \sum_{n\geq 1} H_{n}\frac{\sin n}{n} \), unde

\( H_{n}=1+\frac{1}{2}+\ldots +\frac{1}{n} \).
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.
aleph
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Post by aleph »

Se poate utiliza criteriul lui Abel pentru şirurile \( H_n/n (\searrow 0) \)
şi \( \sin n \) (su sume parţiale mărginite).
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