Real Analysis – Concrete Sequence of Rationals Converging to an Irrational Number and Vice Versa

Question

Give a concrete sequence of rationals which converges to an irrational number and vice versa….

My work

I could give a sequence of irrationals which converges to a rational number…

Let $r\in \mathbb Q,$ $$a_n=\frac {\sqrt 2} n+r$$
But I couldn't give a sequence of rationals which converges to an irrational.. Help me to work out…..

Answer 1

$a_n = \left( 1 +\dfrac{1}{n} \right)^n $ converges to $e$