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Paraguay Mathematical Olympiad
2011 Paraguay Mathematical Olympiad
1
Sum of an expression
Sum of an expression
Source: Paraguayan National Olympiad 2011, Level 3, Problem 1
August 31, 2014
algebra proposed
algebra
Problem Statement
Find the value of the following expression:
1
2
+
(
1
3
+
2
3
)
+
(
1
4
+
2
4
+
3
4
)
+
…
+
(
1
1000
+
2
1000
+
…
+
999
1000
)
\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})
2
1
+
(
3
1
+
3
2
)
+
(
4
1
+
4
2
+
4
3
)
+
…
+
(
1000
1
+
1000
2
+
…
+
1000
999
)
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