I'm trying to prove that the sequence(adsbygoogle = window.adsbygoogle || []).push({});

[tex]x_1,x_2,_\cdots[/tex]

of real numbers, where

[tex]x_1=1[/tex] and [tex]x_{n+1}=x_n+\frac{1}{x_n^2}[/tex] for each [tex]n=1,2, \cdots[/tex]

is unbounded.

(sorry for the ugly latex! i don't know if there's a way to format that better)

I'm thinking of proving by contradiction, assuming it is bounded and then somehow getting it to imply that the sequence is not increasing, but I'm not sure how to go about it.

Any hints?

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# Proving a monotonic sequence is unbounded

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