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Day 2, Problem 3
IMC 2011 · Problem 3
Day 2
18th IMC · Blagoevgrad, Bulgaria
Statement
Determine the value of
∑
n
=
1
∞
ln
(
1
+
1
n
)
⋅
ln
(
1
+
1
2
n
)
⋅
ln
(
1
+
1
2
n
+
1
)
.
\sum_{n=1}^{\infty} \ln\left( 1 + \frac{1}{n} \right) \cdot \ln\left( 1 + \frac{1}{2n} \right) \cdot \ln\left( 1 + \frac{1}{2n+1} \right).
n
=
1
∑
∞
ln
(
1
+
n
1
)
⋅
ln
(
1
+
2
n
1
)
⋅
ln
(
1
+
2
n
+
1
1
)
.
Official solution
Reveal
Hidden so you can work on the problem first.
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