sum of $(\sqrt[n]{3} - 2)^{n}$

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.

• $n$th term test for divergence? – tilper Nov 27 '17 at 16:08

Hint: Is $\lim_{n\to\infty} (\sqrt[n]{3}-2)^n\stackrel{?}{=}0$