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India Pre-Regional Mathematical Olympiad
2018 India PRMO
16
Interesting Summation
Interesting Summation
Source:
June 8, 2019
algebra.
Problem Statement
What is the value of
∑
1
≤
i
<
j
≤
10
(
i
+
j
)
i
+
j
=
o
d
d
{ \sum_{1 \le i< j \le 10}(i+j)}_{i+j=odd}
∑
1
≤
i
<
j
≤
10
(
i
+
j
)
i
+
j
=
o
dd
−
∑
1
≤
i
<
j
≤
10
(
i
+
j
)
i
+
j
=
e
v
e
n
- { \sum_{1 \le i< j \le 10}(i+j)}_{i+j=even}
−
∑
1
≤
i
<
j
≤
10
(
i
+
j
)
i
+
j
=
e
v
e
n
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