Answer
Convergent
Work Step by Step
$\lim\limits_{n \to \infty} \sqrt[n] a_{n}=\lim\limits_{n \to \infty} \sqrt[n] {(\sqrt[n] {2-1)^{n}}}$
$=\lim\limits_{n \to \infty}(\sqrt[n] 2-1)$
$=\lim\limits_{n \to \infty}( 2^{1/n}-1)$
$=1-1$
$=0$
The series is convergent.
