[Toán11] Tìm số hạng tổng quát của dãy Un

M

meanproialy

K

kirisaki

[TEX]u_{n+1} = 3u_{n} + n \Rightarrow u_{n+1} + \frac{n}{2} = 3. \left( u_n + \frac{n}{2} \right) \\ \text{Dat} v_n = u_n + \frac{n}{2} \Rightarrow v_{n+1} = u_{n+1} + \frac{n}{2} \\ \text{Ta co day so Vn thoa man:} v_{n+1} = 3v_n \Rightarrow \left( v_n \right) \text{la cap so nhan vs q=3, v1 = u1 + n/2 = 4 + n/2} \\ \Rightarrow v_n = v_1 . q^{n-1} = \left( 4 + \frac{n}{2} \right) . 3^{n-1} \\ \text{Tu cong thuc} v_n = u_n + \frac{n}{2} \Rightarrow u_n = v_n - \frac{n}{2} = \left( 4 + \frac{n}{2} \right) . 3^{n-1} - \frac{n}{2}[/TEX]
 
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