Answer
$\lim\limits_{n \to \infty} a_n=6$ and {$a_n$} is convergent.
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty}
(2-\dfrac{1}{2^n})(3+\dfrac{1}{2^n})$
$=\lim\limits_{n \to \infty} (2-\dfrac{1}{2^n}) \cdot \lim\limits_{n \to \infty} (3+\dfrac{1}{2^n})$
$=2 \cdot 3$
or, $=6$
Thus, $\lim\limits_{n \to \infty} a_n=6$ and {$a_n$} is convergent.
