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Iran MO (3rd Round)
2001 Iran MO (3rd Round)
2
2
Part of
2001 Iran MO (3rd Round)
Problems
(1)
A real sequence
Source: Iran National Olympiad (3rd Round) 2001
7/13/2007
Does there exist a sequence
{
b
i
}
i
=
1
∞
\{b_{i}\}_{i=1}^\infty
{
b
i
}
i
=
1
∞
of positive real numbers such that for each natural
m
m
m
:
b
m
+
b
2
m
+
b
3
m
+
⋯
=
1
m
b_{m}+b_{2m}+b_{3m}+\dots=\frac1m
b
m
+
b
2
m
+
b
3
m
+
⋯
=
m
1
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