Limita de sir integral cu radicali
Posted: Tue Dec 04, 2007 7:56 am
Sa se arate ca
\( \lim_{n\to\infty} n^{2}\left(\int_0^1\sqrt[n]{1+x^{n}}dx-1\right)=\frac{\pi^2}{12}. \)
Vojtech Jarnik, 2002, Categoria II
\( \lim_{n\to\infty} n^{2}\left(\int_0^1\sqrt[n]{1+x^{n}}dx-1\right)=\frac{\pi^2}{12}. \)
Vojtech Jarnik, 2002, Categoria II