Answer
Converges to $0$
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (\dfrac{1}{3})^n+\dfrac{1}{\sqrt 2^n}$
Since, $ \lim\limits_{n \to \infty} x^n=0$
So, $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (\dfrac{1}{3})^n+\dfrac{1}{\sqrt 2^n}=\lim\limits_{n \to \infty} [(\dfrac{1}{3})^n+(\dfrac{1}{\sqrt 2})^n]=0$
Hence, $\lim\limits_{n \to \infty} a_n=0$ and {$a_n$} is Convergent and converges to $0$
