MathDB
Problems
Contests
International Contests
IMO Longlists
1970 IMO Longlists
9
Algebraic Sum - ILL 1970 - Problem 9.
Algebraic Sum - ILL 1970 - Problem 9.
Source:
May 24, 2011
induction
Problem Statement
For even
n
n
n
, prove that
∑
i
=
1
n
(
(
−
1
)
i
+
1
⋅
1
i
)
=
2
∑
i
=
1
n
/
2
1
n
+
2
i
\sum_{i=1}^{n}{\left((-1)^{i+1}\cdot\frac{1}{i}\right)}=2\sum_{i=1}^{n/2}{\frac{1}{n+2i}}
∑
i
=
1
n
(
(
−
1
)
i
+
1
⋅
i
1
)
=
2
∑
i
=
1
n
/2
n
+
2
i
1
.
Back to Problems
View on AoPS