Below are some practice problems with a subjective rating on difficulties. The solutions are included at the end of Math Olympiad part of LibreNotebook.
0.1.1. 2000 APMO Problem 1 (\(\bullet \bullet \circ \)) Find \(S = \sum _{i=0}^{101} \frac {x_i^3}{1 - 3x_i + 3x_i^2}\) for \(x_i = \frac {i}{101}\).