# Limiting factorials

Calculus Level 4

$\large \lim_{ n \to\infty }{ \left( \frac{ 5n \choose 3n }{ 3n \choose 2n } \right) }^{1/n} =\frac{ { a }^{ a } }{ { b }^{ 2b } }$

The equation above holds true for positive integers $$a$$ and $$b$$. Find the value of $$a+b$$.


Bonus: Do it without Stirling's approximation.

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