2
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Which convergence tests should I use here? I know it diverges.

$\sum_{n=0}^\infty (\sqrt[n]{3} - 2)^{n}$

I've tried root and condensation tests but it led me nowhere.

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  • $\begingroup$ $n$th term test for divergence? $\endgroup$ – tilper Nov 27 '17 at 16:08
4
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Hint: Is $\lim_{n\to\infty} (\sqrt[n]{3}-2)^n\stackrel{?}{=}0$

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    $\begingroup$ @samjoe I guess limit isn't zero $\endgroup$ – openspace Nov 27 '17 at 16:14
  • $\begingroup$ Not sure why this was downvoted, but it's the right question to ask. (@samjoe: Double-check your limit.) $\endgroup$ – Aaron Montgomery Nov 27 '17 at 16:23
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    $\begingroup$ @Aaron Oh I understand it is oscillatory! $\endgroup$ – samjoe Nov 27 '17 at 16:26
  • $\begingroup$ I didnt downvote, but have upvoted him now $\endgroup$ – samjoe Nov 27 '17 at 16:29

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