Answer
$\lim\limits_{n \to \infty} a_n=2 $ and {$a_n$} is convergent.
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty}[2+(0.1)^n]=\lim\limits_{n \to \infty} (2)+\lim\limits_{n \to \infty} (0.1)^n$
or, $=2+0$
or, $=2$
Thus, $\lim\limits_{n \to \infty} a_n=2 $ and {$a_n$} is convergent.
