Evaluating $\lim\limits_{n\to\infty}\{(2+ \sqrt{3})^n\}$, where $\{x\}$ is the fractional part of $x$
How to compute $\lim\limits_{n\rightarrow \infty} \{(2+\sqrt{3})^{n}\}$, where $\{x\}$ is the fractional part of $x$?