Consider [itex]x_1,y_1 \in \mathbb{R}[/itex] such that [itex]x_1>y_1>0[/itex] and [itex]\{x_n\},\{y_n\}[/itex] the two sequences defined for all naturals by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x_{n+1}=\frac{x_n+y_n}{2}, \ \ \ \ \ y_{n+1}=\sqrt{x_n y_n}[/tex]

Show that the sequence [itex]\{y_n\}[/itex] is increasing and as [itex]x_1[/itex] for an upper bound.

I would appreciate some help on this one, I have made no progress.

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# Two sequences defined for all naturals by

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