Hint for $\lim_{n\rightarrow\infty} \sqrt[n]{\prod_{i=1}^n\frac{1}{\cos\frac{1}{i}}}$. How to calculate the following limit:
$$\lim_{n\rightarrow\infty}\sqrt[n]{\prod_{i=1}^n\frac{1}{\cos\frac{1}{i}}}$$
thanks.

Hint:
$$\lim_{n \to \infty} a_n ^{1/n} = \lim_{n \to \infty} \frac{a_{n+1}}{a_n},$$
and
$$\lim_{n \to \infty} \frac{1}{\cos[1/(n+1)]} = 1$$
