I've encountered this limit :
$$\lim_{n\to\infty} \frac1n \left(\sin\left(\frac{\pi}{n}\right) + \sin\left(\frac{2\pi}{n}\right)+\cdots+\sin{\frac{(n-1)\pi}{n}}\right)$$
Wolfram gives the value: $2\over \pi$.
We did something similar in class. If I consider the function: $\sin(x\pi)$ and the equidistant partition: $j\over n$, I can somehow transform this problem into an integral.
Could someone please give me some advices and\or guidance on how to proceed in this problem.
Thanks for any suggestions in advance.
edit: Thanks a lot guys.