# Too much pi

Calculus Level 4

$\large \lim_{n\to \infty }\left[ \dfrac{n}{2} \left( 2\sqrt[n]{\dfrac{\pi }{2} } -\sqrt[n]{\dfrac{\pi }{3} } -\sqrt[n]{\dfrac{\pi }{4} } \right) \right] =\dfrac{\ln A }{B}$

If the equation above holds true for positive integers $$A$$ and $$B$$, such that $$A$$ is minimized, find $$A+B$$.

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