\(\pi\) is everywhere!

Calculus Level 4

\[ \large \lim_{n\to \infty} \dfrac{ (2n-1)!!}{(2n)!!} \sqrt n \]

Given that the limit above is equal to \( \pi^{-A /B} \), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).

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