Answer
Diverges
Work Step by Step
Let us consider $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (1-\dfrac{3}{n})^n$
This can be written as: $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} (1+(-\dfrac{3}{n}))^n$
$\implies \lim\limits_{n \to \infty} a_n=e^{-3}=\dfrac{1}{e^3}$
Therefore, $\lim\limits_{n \to \infty} a_n \ne 0$
Thus, the Series diverges and $\lim\limits_{n \to \infty} a_n=\dfrac{1}{e^3}$
