Doua limite cu sirul armonic
Posted: Mon Nov 05, 2007 1:36 am
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
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