# Math Help - analysis!!

1. ## analysis!!

Let ${x_n \ be \ a \ bounded \ sequence \ ,\ for \ m \ \in N , \ let \ y_m = sup \{x_n ; n \geq m \}}$
$show \ that \ y_m \ is \ convergent$$\mbox {x_1 =a , x_2 =b , and x_n= \frac {1}{3} x_{n-1} + \frac {2}{3} x_{n-2}; n \geq 3 }$

2. Originally Posted by flower3
Let $(x_n)$ be a bounded sequence. For $m \in N$, let $y_m = \sup \{x_n ; n \geq m \}$.
Show that $(y_m)$ is convergent.$\mbox {x_1 =a , x_2 =b , and x_n= \frac {1}{3} x_{n-1} + \frac {2}{3} x_{n-2}; n \geq 3 }$
Hint: Show that $(y_m)$ is a decreasing sequence that is bounded below.