27024: Revision history

9 June 2024

• curprev 17:3517:35, 9 June 2024‎ Andrei.Horvat talk contribs‎ 1,057 bytes +1‎ No edit summary undo Tag: visualeditor
• curprev 17:3517:35, 9 June 2024‎ Andrei.Horvat talk contribs‎ 1,056 bytes +33‎ No edit summary undo Tag: visualeditor

16 January 2024

• curprev 08:2808:28, 16 January 2024‎ Andrei.Horvat talk contribs‎ 1,023 bytes −19‎ No edit summary undo Tag: visualeditor

5 December 2023

• curprev 15:5215:52, 5 December 2023‎ Robert Manc talk contribs‎ 1,042 bytes +49‎ No edit summary undo
• curprev 15:2815:28, 5 December 2023‎ Robert Manc talk contribs‎ 993 bytes +993‎ Pagină nouă: '''27024 (Gheorghe Szöllösy)''' ''Fie '' <math> I_n = \int_{0}^{\pi} \frac{\cos nx}{13-12\cos x}\,dx, n\ge0.</math>'' Să se calculeze '' <math>\lim_{n \to \infty}(I_0+I_1+I_2+\ldots+I_n).</math> '''Soluție. ''' ''Să observăm că'' <math>I_{n+2}+I_n = \int_{0}^{\pi}\frac{2\cos x-\cos(n_1)x}{13-12\cos x}\,dx = \frac{1}{6}\int_{0}^{\pi}\frac{(12\cos x-13+13)\cos(n+1)x}{13-12\cos x}\,dx= =\frac{1}{6(n+1)}\sin(n+1)x\Biggr|_{0}^{\pi}+\frac{13}{6}I_{n+1}, </math>'' oricare...