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Mediterranean Mathematics Olympiad
2008 Mediterranean Mathematics Olympiad
3
Calculate the Sum
Calculate the Sum
Source: 2008 MMO Problem #3
September 13, 2011
algebra unsolved
algebra
Problem Statement
Let
n
n
n
be a positive integer. Calculate the sum
∑
k
=
1
n
∑
1
≤
i
1
<
…
<
i
k
≤
n
2
k
(
i
1
+
1
)
(
i
2
+
1
)
…
(
i
k
+
1
)
\sum_{k=1}^n\ \ {\sum_{1\le i_1 < \ldots < i_k\le n}^{}{\frac {2^k}{(i_1 + 1)(i_2 + 1)\ldots (i_k + 1)}}}
∑
k
=
1
n
∑
1
≤
i
1
<
…
<
i
k
≤
n
(
i
1
+
1
)
(
i
2
+
1
)
…
(
i
k
+
1
)
2
k
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