O limita cu sirul armonic

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Cezar Lupu
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O limita cu sirul armonic

Post by Cezar Lupu »

Sa se calculeze \( \lim_{n\to\infty} e^{H_{n+1}}-e^{H_{n}} \), unde \( H_{n}=1+\frac{1}{2}+\ldots +\frac{1}{n} \) este sirul armonic.
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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Radu Titiu
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Post by Radu Titiu »

E echivalenta cu :

\( \lim_{n}\frac{e^{H_{n}}}{n+1}\cdot \frac{e^{\frac{1}{n+1}}-1}{\frac{1}{n+1}}= \lim_{n} (e^{H_{n}-\ln(n)})\cdot \frac{n}{n+1}=e^c \) ,unde c este constanta lui Euller
A mathematician is a machine for turning coffee into theorems.
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