Sequence ${u_n}$ is defined with $u_0=0,u_1=\frac{1}{3}$ and $$\frac{2}{3}u_n=\frac{1}{2}(u_{n+1}+u_{n-1})$$$\forall n=1,2,...$ Show that $|u_n|\leq1$ $\forall n\in\mathbb{N}.$
Source: 2nd Test - Indonesia TST IMO 2010 Training Camp P1
Tags: Sequence, algebra
Sequence ${u_n}$ is defined with $u_0=0,u_1=\frac{1}{3}$ and $$\frac{2}{3}u_n=\frac{1}{2}(u_{n+1}+u_{n-1})$$$\forall n=1,2,...$ Show that $|u_n|\leq1$ $\forall n\in\mathbb{N}.$