determine the monotonicity of [itex]a_n=\frac{n-1}{n}[/tex](adsbygoogle = window.adsbygoogle || []).push({});

heres my work...

[tex]\frac{a_{n+1}}{a_n}=\frac{ \frac{n}{n+1}}{\frac{n-1}{n}}[/tex]

[tex]=\frac{n^2}{n^2-1}>1[/tex]

Therefore the sequence is monotone increasing.

But...when you look at the original expression for a_n, it looks like it is always LESS than one...does this impact anything at all?

Josh

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# Monotonicity of a sequence

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