Answer
Sequence converges to $0$.
Work Step by Step
As we know that a sequence converges when $\lim\limits_{n \to \infty}a_n$ exists.
Consider $a_n=\dfrac{1-(-1)^n}{\sqrt n}$
Apply limits to both sides.
$\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}[\dfrac{1-(-1)^n}{\sqrt n}]$
Using Sandwich Theorem:
$\lim\limits_{n \to \infty}a_n=\lim\limits_{n \to \infty}\dfrac{2}{\sqrt n}$
$\lim\limits_{n \to \infty}a_n=\dfrac{2}{\sqrt \infty}$
$\lim\limits_{n \to \infty}a_n=\dfrac{2}{ \infty}$
$\lim\limits_{n \to \infty}a_n=0$
Hence, the sequence converges to $0$.
