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2015 VTRMC
Problem 4
Problem 4
Part of
2015 VTRMC
Problems
(1)
surjectivity of sum of subseries of harmonic series
Source: VTRMC 2015 P4
5/5/2021
Consider the harmonic series
∑
n
≥
1
1
n
=
1
+
1
2
+
1
3
+
…
\sum_{n\ge1}\frac1n=1+\frac12+\frac13+\ldots
∑
n
≥
1
n
1
=
1
+
2
1
+
3
1
+
…
. Prove that every positive rational number can be obtained as an unordered partial sum of this series. (An unordered partial sum may skip some of the terms
1
k
\frac1k
k
1
.)
series