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[tex] \lim_{n\rightarrow \infty}\left( \frac{1}{n}\cdot\sum_{i=1}^{n}\sqrt{1-\frac{i^{2}}{n^{2}}}\right)= \frac{\pi}{4} [/tex]

So, how do I show this. Can I do it with an integral (as Dextercioby did)?

This limit came out when I was triyng to derive the formula of the surface area of a sphere in the way Archimedes did.