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2014 BMT Team 16
Source:
January 6, 2022
algebra
Problem Statement
Evaluate
∑
n
=
0
∞
∑
k
=
0
∞
min
(
n
,
k
)
(
1
2
)
n
(
1
3
)
k
\sum_{n=0}^{\infty} \sum_{k=0}^{\infty} \min (n, k) \left( \frac12 \right)^n\left( \frac13 \right)^k
n
=
0
∑
∞
k
=
0
∑
∞
min
(
n
,
k
)
(
2
1
)
n
(
3
1
)
k
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