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sum 1/a_n 1 < 29

Source: Polish MO Finals 1971 p1

August 22, 2024
algebranumber theoryinequalities

Problem Statement

Show that if (an)(a_n) is an infinite sequence of distinct positive integers, neither of which contains digit 00 in the decimal expansion, then ∑n=1∞1an<29.\sum_{n=1}^{\infty} \frac{1}{a_n}< 29.
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