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20
Math Prize 2022 Problem 20
Math Prize 2022 Problem 20
Source:
October 12, 2022
Problem Statement
Let
a
n
=
n
(
2
n
+
1
)
a_n = n(2n+1)
a
n
=
n
(
2
n
+
1
)
. Evaluate
∣
∑
1
≤
j
<
k
≤
36
sin
(
π
6
(
a
k
−
a
j
)
)
∣
.
\biggl | \sum_{1 \le j < k \le 36} \sin\bigl( \frac{\pi}{6}(a_k-a_j) \bigr) \biggr |.
1
≤
j
<
k
≤
36
∑
sin
(
6
π
(
a
k
−
a
j
)
)
.
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