$$\lim_{n\rightarrow\infty}\sum_{r=1}^n \sin\left(\frac{r}{n} \right)=\lim_{n\rightarrow\infty} \left[\sin\frac{1}{n}+\sin\frac{2}{n}+\cdots+\sin(1)\right]=0+0+\cdots+\sin(1)=1$$
Could anybody explain why this is wrong? I've tried to see why this doesn't work but I don't see why not. Thank you.
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