Limit Problem

Level pending

\[\lim _{n \to\infty}\left(\frac{\binom{3n}{n}}{\binom{2n}{n}}\right)^ \left(\frac{1}{n}\right)\]

can be expressed in the form \(\frac{a}{b}\), where \(a\) and \(b\) are coprime numbers. What is the value of a+b?

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