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Vojtěch Jarník IMC
2011 VJIMC
Problem 2
k-repeated sum
k-repeated sum
Source: VJIMC 2011 2.2
June 1, 2021
Summation
algebra
Problem Statement
Let
k
k
k
be a positive integer. Compute
∑
n
1
=
1
∞
∑
n
2
=
1
∞
⋯
∑
n
k
=
1
∞
1
n
1
n
2
⋯
n
k
(
n
1
+
n
2
+
…
+
n
k
+
1
)
.
\sum_{n_1=1}^\infty\sum_{n_2=1}^\infty\cdots\sum_{n_k=1}^\infty\frac1{n_1n_2\cdots n_k(n_1+n_2+\ldots+n_k+1)}.
n
1
=
1
∑
∞
n
2
=
1
∑
∞
⋯
n
k
=
1
∑
∞
n
1
n
2
⋯
n
k
(
n
1
+
n
2
+
…
+
n
k
+
1
)
1
.
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