We show that there exists a positive constant $C$ such that the following holds: Given an infinite arithmetic progression $\A$ of real numbers and a sufficiently large integer $n$ (depending on $\A$), there needs at least $Cn$ geometric progressions to cover the first $n$ terms of $\A$. A similar result is presented, with the role of arithmetic and geometric progressions reversed.
Covering an arithmetic progression with geometric progressions and vice versa
SANNA, CARLO
2014-01-01
Abstract
We show that there exists a positive constant $C$ such that the following holds: Given an infinite arithmetic progression $\A$ of real numbers and a sufficiently large integer $n$ (depending on $\A$), there needs at least $Cn$ geometric progressions to cover the first $n$ terms of $\A$. A similar result is presented, with the role of arithmetic and geometric progressions reversed.
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