Doua limite cu sirul armonic

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Cezar Lupu
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Doua limite cu sirul armonic

Post by Cezar Lupu »

Fie sirul armonic \( H_{n}=1+\frac{1}{2}+\ldots +\frac{1}{n} \), \( n\geq 1 \). Sa se calculeze:

i) \( \lim_{n\to\infty}(\sqrt[n]{H_{n}})^{H_{n}} \);

ii) \( \lim_{n\to\infty}\frac{n}{ln^{2} n}\left[(\sqrt[n]{H_{n}})^{H_{n}}-1\right] \).


Cezar Lupu, R.M.I. C-ta, 2004
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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