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

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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