Answer
converges to $e^{-1}$
Work Step by Step
As we know that $\lim\limits_{n \to \infty} (1+\dfrac{x}{n})^{n}=e^x$ when $x \gt 0$
Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} (1-\dfrac{1}{n})^{n}$
This implies that $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty} (1-\dfrac{1}{n})^{n}=\lim\limits_{n \to \infty} (1+(-\dfrac{1}{n}))^{n}\implies a_n=e^{-1}$
Thus, $\lim\limits_{n \to \infty} a_n=e^{-1}$ and {$a_n$} converges to $e^{-1}$.
