Does this limit $lim_{n\to\infty}\sum_{i=0}^n 1/n \sqrt{1 - i^2/n^2}$ converge to $\pi/4$? While trying to find an approximate area of a quarter of a circle by splicing it into small rectangles and summing their areas I've reached a point where I have this formula:
$$\sum_{i=0}^n 1/n \sqrt{1 - i^2/n^2}$$
Writing quick program and calculating the sum with n = 100, 100, 1000, 10k, 100k items suggest this sum converges to $\pi/4$, however I have no idea why. I've tried to search for known series converging to $\pi/4$ but nothing seems to resemble above formula.
Please note that in this question I'm not interested in what I was initially for, i.e. the area of a quarter of a circle. This was merely an exercise to show my nephew how we can approximate certain things.

This directly leads from fundamental theorem of calculus (https://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus) and the definition of Reimannian sum (https://en.wikipedia.org/wiki/Riemann_sum)
