Let $\displaystyle f_n(x) = \cos^n x$
and $\displaystyle g(x) = \lim_{n\rightarrow \infty} \sum_{k = 0}^{n} \left(\frac{x}{4}\right)$
If $\displaystyle g(x)$ is continuous in $\displaystyle (0,c)$ then find the largest value of $\displaystyle c$.
Let $\displaystyle f_n(x) = \cos^n x$
and $\displaystyle g(x) = \lim_{n\rightarrow \infty} \sum_{k = 0}^{n} \left(\frac{x}{4}\right)$
If $\displaystyle g(x)$ is continuous in $\displaystyle (0,c)$ then find the largest value of $\displaystyle c$.