Binomial limit

Calculus Level 4

limn((3nn)(2nn))1n=ab\large \lim_{n \to \infty} \left(\frac{\binom{3n}{n} }{\binom{2n}{n} }\right) ^{\frac{1}{n}} = \frac{a}{b}

The equation above holds true for coprime integers aa and bb. What is a+ba+b?

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