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2010 IMC
2
IMC 2010 - Problem 2
IMC 2010 - Problem 2
Source:
July 26, 2010
integration
logarithms
real analysis
infinite series
Problem Statement
Compute the sum of the series
∑
k
=
0
∞
1
(
4
k
+
1
)
(
4
k
+
2
)
(
4
k
+
3
)
(
4
k
+
4
)
=
1
1
⋅
2
⋅
3
⋅
4
+
1
5
⋅
6
⋅
7
⋅
8
+
.
.
.
\sum_{k=0}^{\infty} \frac{1}{(4k+1)(4k+2)(4k+3)(4k+4)} = \frac{1}{1\cdot2\cdot3\cdot4} + \frac{1}{5\cdot6\cdot7\cdot8} + ...
∑
k
=
0
∞
(
4
k
+
1
)
(
4
k
+
2
)
(
4
k
+
3
)
(
4
k
+
4
)
1
=
1
⋅
2
⋅
3
⋅
4
1
+
5
⋅
6
⋅
7
⋅
8
1
+
...
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