Cho Un = sin(2n-1).pi/3
a.CMR Un = U(n+3)
b.Tính S17
[TEX]U_{n+3} = sin \bigg( (2n + 5 ) \frac{\pi}{3} \bigg) = sin \bigg( ( 2n -1) \frac{\pi}{3} - 2 \pi \bigg) = U_n[/TEX]
Áp dụng câu a:
[TEX]S_{17} = U_1 + ...+ U_{17} = 6U_1 + 6 U_2 + 5U_3 = 6. sin {\frac{\pi}{3}} + 6 sin \pi + 5. sin {\frac{5\pi}{3} = \frac{\sqrt{3}}{2} [/TEX] chú ý : [TEX]sin {\frac{5\pi}{3}} = sin ( - \frac{\pi}{3}) = - sin {\frac{\pi}{3}}[/TEX]