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