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Evaluate

$\lim_{N\to\infty} \left(\frac{1}{2N}+\frac{1}{2N+1}+\frac{1}{2N+2}+\frac{1}{2N+3}+\dots+\frac{1}{3N}\right).$

The answer is of the form $\ln \frac{a}{b},$ where $a$ and $b$ are coprime positive integers.

Find $a+b$.

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