(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

3. 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.

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# Homework Help: Proof about a sequence.

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