Binomials and Limits

Calculus Level 3

Define a relation $$f:\Bbb{Z^+}\mapsto\Bbb{R^+}$$ given by:

$f(n)=4^n\cdot \frac{\dbinom{2n}{n}}{\dbinom{4n}{2n}}$

Find the value of the following limit:

$\lim_{n\to\infty}f(n)$

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