HMMT 2010 K4

Compute $\lim _{n \rightarrow \infty} \frac{\sum_{k=1}^{n}|\cos (k)|}{n}$ .

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

\frac{2}{\pi}

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.