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Purple Comet Problems
2003 Purple Comet Problems
11
Problem 11, Fall 2003 , MS and HS
Problem 11, Fall 2003 , MS and HS
Source:
June 23, 2011
Problem Statement
If
1
1
+
2
+
1
1
+
2
+
3
+
…
+
1
1
+
2
+
…
+
20
=
m
n
\frac{1}{1+2} + \frac{1}{1+2+3} + \ldots + \frac{1}{1+2 + \ldots + 20} = \frac{m}{n}
1
+
2
1
+
1
+
2
+
3
1
+
…
+
1
+
2
+
…
+
20
1
=
n
m
where
m
m
m
and
n
n
n
are positive integers with no common divisor, find
m
+
n
m + n
m
+
n
.
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