Inspired by earlier post of mine, Fibonacci but with ratio of sum and difference of previous two terms
$$a_0=a_1=1$$ $$a_n = \frac{1}{a_{n-1}} + \frac{1}{a_{n-2}}$$
Unlike my earlier variant which doesn't converge to constant and is very messy, this sequence converge to $\sqrt{2}$. Like the earlier question of mine, i seek a closed-form formula analogous to the Binet's formula for regular Fibonacci sequence.