(adsbygoogle = window.adsbygoogle || []).push({}); Another convergence/divergence question :)

Hi, thank you in advance for your help. This was a practice problem for the New Jersey Undergraduate Mathematics Competition last year.

Prove whether or not the following converges:

[tex]\sqrt{1+\sqrt{2+\sqrt{3+...}}}[/tex]

Forgive my LaTeX, I'm still learning :). Suggestions on that would be appreciated as well, haha.

For this problem, I was thinking of reducing it to the following:

[tex]\sqrt{\sqrt\ ... \sqrt{n}}[/tex]

which reduces to [tex]n^{1/n}[/tex],

which I would then show diverges, because I think it does diverge, but I'm just not sure.

Thanks for the help.

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# Another convergence/divergence question

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