- #1
cragar
- 2,552
- 3
Homework Statement
Show that the sequence [itex] (x_1,x_2,x_3,...) [/itex]
defined by; Let [itex] x_1=1 [/itex] for each [itex] n \in \mathbb{N} [/itex]
[itex] x_{n+1}= \frac{x_n}{2}+1 [/itex]
[itex] x_2=\frac{3}{2} [/itex]
Show that this sequence is bounded above by 2; that is prove that [itex] x_n\leq2 [/itex] for all [itex] n\in\mathbb{N} [/itex]
The Attempt at a Solution
This seems weird to me because it doesn't seem like it would be bounded above by 2, I could find some x that was bigger that 2. unless I don't understand the question.