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4
Math Prize 2012 Problem 4
Math Prize 2012 Problem 4
Source:
September 24, 2012
Problem Statement
Evaluate the expression
121
(
1
13
−
1
17
)
+
169
(
1
17
−
1
11
)
+
289
(
1
11
−
1
13
)
11
(
1
13
−
1
17
)
+
13
(
1
17
−
1
11
)
+
17
(
1
11
−
1
13
)
.
\frac{121 \left( \frac{1}{13} - \frac{1}{17} \right) + 169 \left( \frac{1}{17} - \frac{1}{11} \right) + 289 \left( \frac{1}{11} - \frac{1}{13} \right)}{ 11 \left( \frac{1}{13} - \frac{1}{17} \right) + 13 \left( \frac{1}{17} - \frac{1}{11} \right) + 17 \left( \frac{1}{11} - \frac{1}{13} \right)} \, .
11
(
13
1
−
17
1
)
+
13
(
17
1
−
11
1
)
+
17
(
11
1
−
13
1
)
121
(
13
1
−
17
1
)
+
169
(
17
1
−
11
1
)
+
289
(
11
1
−
13
1
)
.
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