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7
HMMT Algebra/NT 2019/7: A non-symmetric three-variable infinite sum
HMMT Algebra/NT 2019/7: A non-symmetric three-variable infinite sum
Source:
February 17, 2019
HMMT
algebra
Summation
Problem Statement
Find the value of
∑
a
=
1
∞
∑
b
=
1
∞
∑
c
=
1
∞
a
b
(
3
a
+
c
)
4
a
+
b
+
c
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
.
\sum_{a = 1}^{\infty} \sum_{b = 1}^{\infty} \sum_{c = 1}^{\infty} \frac{ab(3a + c)}{4^{a+b+c} (a+b)(b+c)(c+a)}.
a
=
1
∑
∞
b
=
1
∑
∞
c
=
1
∑
∞
4
a
+
b
+
c
(
a
+
b
)
(
b
+
c
)
(
c
+
a
)
ab
(
3
a
+
c
)
.
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