Let \(\displaystyle f(x)= \lim_{n \rightarrow \infty} \left(\cos \left(\frac{x}{\sqrt{n}}\right)\right)^{n}\) and \(\displaystyle g(x) = \dfrac{-1}{2\ln (f(x))}\).

The value of \(\displaystyle \sum_{n = 1}^{\infty} g(n)\) has a closed form. Find this closed form.

Give your answer to 3 decimal places.

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