How can I find limit points of $\{2^n \sqrt 2\},$$\{2^n \sqrt 2\}$, where $\{\cdot\}$ denotes the fractional part function? This ais a subsequence of the sequence $\{\sqrt n\}$ for which we know the set of limit points. However, it is not clear to me if $\{2^n \sqrt 2\}$ converge or has several limit points. Thanks!