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

The answer is 0.428.

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