Cool Summation!! (Hint: Fundamental something something)

Calculus Level 4

\[\lim_{n \to \infty} \left[\ln \left(\sqrt[n]{\frac{4}{n^2}}\right) + \ln\left(\sqrt[n]{\frac{16}{n^2}}\right) + \ln\left(\sqrt[n]{\frac{36}{n^2}}\right)+ \cdots + \ln\left(\sqrt[n]{\frac{4n^2}{n^2}}\right) \right]=\ ?\]

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