Sequence Of Nested Open Interval Provide an example of a sequence of nested open intervals $((an,bn))_{n=1}^{+\infty}$, $a_{n+1},b_{n+1} \subset(a_{n},b_{n})$, such that $∩_{n=1}^{\infty} (a_{n},b_{n}) = \emptyset$

Solution Attempt:

$[n,\infty)$
Take $a_n = 0, b_n = \dfrac{1}{n}, \forall n \ge 1$
$$b_n=1$$

$$a_n=1-\frac 2n$$

$\forall \epsilon&lt;1$, for $n$ great enough,

$$1-\frac 2n&gt;\epsilon.$$