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India Pre-Regional Mathematical Olympiad
2017 India PRMO
6
2017 preRMO p6, \sum_{n=1}^{9} \1/n(n+1)(n+2)
2017 preRMO p6, \sum_{n=1}^{9} \1/n(n+1)(n+2)
Source:
August 9, 2019
Sum
algebra
Problem Statement
Let the sum
∑
n
=
1
9
1
n
(
n
+
1
)
(
n
+
2
)
\sum_{n=1}^{9} \frac{1}{n(n+1)(n+2)}
∑
n
=
1
9
n
(
n
+
1
)
(
n
+
2
)
1
written in its lowest terms be
p
q
\frac{p}{q}
q
p
. Find the value of
q
−
p
q - p
q
−
p
.
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