Answer
$\lim\limits_{n \to \infty} a_n=1 $ and {$a_n$} is convergent.
Work Step by Step
Consider $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty}
\dfrac{n+(-1)^n}{n}$
or, $=\lim\limits_{n \to \infty} [\dfrac{n}{n}+\dfrac{(-1)^n}{n})$
or, $=\lim\limits_{n \to \infty} 1 +\lim\limits_{n \to \infty} \dfrac{(-1)^n}{n}$
or, $=1+0$
Thus, $\lim\limits_{n \to \infty} a_n=1 $ and {$a_n$} is convergent.
