Answer
converges to $0$
Work Step by Step
As we know that $ \lim\limits_{n \to \infty} x^n=0$
Let $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (\dfrac{1}{3})^n+\dfrac{1}{\sqrt {2^{n}}}$
This implies that $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (\dfrac{1}{3})^n+\dfrac{1}{\sqrt {2^{n}}}$
and $\lim\limits_{n \to \infty} [(\dfrac{1}{3})^n+(\dfrac{1}{\sqrt 2})^n]=0+0=0$
Thus, {$a_n$} is Convergent and converges to $0$.
