Answer
$$0$$
Work Step by Step
Definition of a sequence defined by a function: Let us consider a function $f(x)$ whose limit $\lim\limits_{x \to \infty} f(x)$ exists then the sequence $a_n=f(n)$ will converge to the same limit.
That is, $\lim\limits_{n \to \infty} a_n=\lim\limits_{x \to \infty} f(x)$
Here, we have $a_n=\dfrac{(-1)^n}{n}$ and $f(x)=\dfrac{(-1)^n}{n}$
Next, $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \dfrac{(-1)^n}{n}$
a) When $n$ is odd.
$\lim\limits_{n \to \infty} a_n=\lim\limits_{x \to \infty} \dfrac{-1}{n}=0$
b) When $n$ is even.
$\lim\limits_{n \to \infty} a_n=\lim\limits_{x \to \infty} \dfrac{1}{n}=0$
Thus. $\lim\limits_{n \to \infty} a_n=0$