# College Math

Algebra Level 5

$\large \prod_{k=0}^{\infty}\left(1-\frac1{a_k}\right)$

Consider the recurrence relation $$a_k = a_{k-1} ^2 - 2$$ with $$a_0 = 5/2$$. If the product above can be stated in terms of $$\dfrac AB$$, where $$A$$ and $$B$$ are coprime positive integers, find the value of $$A+B$$.

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