As an example, for the sequence:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]s_{1} =2[/tex]

[tex]s_{n+1}=\frac{s^{2}_{n}+1}{2}[/tex]

We see:

When [tex]s_{n} >1 [/tex] then,

[tex]s_{n+1}=\frac{s^{2}_{n}+1}{2}>s_{n}[/tex]

But how do I formally show that this last inequality is true? This example is fine or just one similar to it. Thanks!

EDIT: Many of those superscripts are suppose to be subscripts. I don't seem to be able to edit them so there correct though. Sorry, hopefully you can still figure it out. If, it doesn't have any subscript at all, then whatever is the superscript is suppose to be the subscript. However, if there is a subscript then the superscript is correct.

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# How do you formally show subsequent element in a series is larger?

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