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Putnam
1984 Putnam
A2
infinite sum involving powers
infinite sum involving powers
Source: Putnam 1984 A2
August 31, 2021
Summation
real analysis
algebra
Problem Statement
Express
∑
k
=
1
∞
6
k
(
3
k
+
1
−
2
k
+
1
)
(
3
k
−
2
k
)
\sum_{k=1}^\infty\frac{6^k}{(3^{k+1}-2^{k+1})(3^k-2^k)}
∑
k
=
1
∞
(
3
k
+
1
−
2
k
+
1
)
(
3
k
−
2
k
)
6
k
as a rational number.
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