Binomial limit

Calculus Level 5

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

The equation above holds true for coprime integers \(a\) and \(b\). What is \(a+b\)?

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