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1

Part of 2011 Paraguay Mathematical Olympiad

Problems(1)

Sum of an expression

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

8/31/2014
Find the value of the following expression:
12+(13+23)+(14+24+34)+…+(11000+21000+…+9991000)\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})
algebra proposedalgebra