Calculus Level pending

Let $$a_{0}=\dfrac{5}{2}$$ and $$a_{k}=a_{k-1}^2 -2$$ for $$k \ge 1$$. Compute :

$\large \displaystyle \prod_{k=0}^{\infty} \left(1- \dfrac{1}{a_{k}} \right)$

in closed form. Answer up to 3 decimal places

×