$\lim_{x \rightarrow \infty} \left[ \cos \left( 2\pi \left( \frac{x}{1+x} \right)^a \right) \right], \quad a \in \mathbb{R}$

Mathematics

Problem

\lim_{x \rightarrow \infty} \left[ \cos \left( 2\pi \left( \frac{x}{1+x} \right)^a \right) \right], \quad a \in \mathbb{R}