Problem

Source: Paraguayan National Olympiad 2011, Level 3, Problem 1

Tags: algebra proposed, algebra



Find the value of the following expression: $\frac{1}{2} + (\frac{1}{3} + \frac{2}{3}) + (\frac{1}{4} + \frac{2}{4} + \frac{3}{4}) + \ldots + (\frac{1}{1000} + \frac{2}{1000} + \ldots + \frac{999}{1000})$