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