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Eotvos Mathematical Competition (Hungary)
1936 Eotvos Mathematical Competition
1
sum 1/(2k-1)2k
sum 1/(2k-1)2k
Source: Eotvos 1936 p1
September 10, 2024
algebra
Sum
number theory
Problem Statement
Prove that for all positive integers
n
n
n
,
1
1
⋅
2
+
1
3
⋅
4
+
.
.
.
+
1
(
2
n
−
1
)
2
n
=
1
n
+
1
1
n
+
2
+
.
.
.
+
1
2
n
\frac{1}{1 \cdot 2}+\frac{1}{3 \cdot 4}+ ...+ \frac{1}{(2n - 1)2n}=\frac{1}{n + 1}\frac{1}{n + 2}+ ... +\frac{1}{2n}
1
⋅
2
1
+
3
⋅
4
1
+
...
+
(
2
n
−
1
)
2
n
1
=
n
+
1
1
n
+
2
1
+
...
+
2
n
1
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