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Calculus Level 5

\[\Gamma{\left(\dfrac{1}{2}\right)} = \sqrt{\pi}\]

Using the fact above, find \(n\) if \(\dfrac{2^{n-1}(2n-1)}{\sqrt{\pi}}\Gamma{\left(\dfrac{2n-1}{2}\right)} = 9999!!\).

\(\)
Notation: \(!!\) denotes the double factorial notation. For example, \(10!!=10\times8\times6\times4\times2 \).

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