calculus - Find $lim_{ntoinfty}left(1-frac{1}{a_n}right)^n$.

Let $(a_n)$ be a strictly increasing sequence of
real numbers such that $a_0\geq 1$ and $a_n\rightarrow \infty$ as $n\rightarrow \infty.$

The following limit is always convergent or which condition may be added on $(a_n)$ the given limit to be convergent?
$$\lim_{n\to\infty}\left(1-\frac{1}{a_n}\right)^n$$