# Sum the cosine limit

Calculus Level 4

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.