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Miklós Schweitzer 1960- Problem 6

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November 21, 2015
college contestsreal analysis

Problem Statement

6. Let {nk}k=1∞\{ n_k \}_{k=1}^{\infty} be a stricly increasing sequence of positive integers such that
lim⁡k→∞nk12k=∞\lim_{k \to \infty} n_k^{\frac {1}{2^k}}= \infty
Show that the sum of the series ∑k=1∞1nk\sum_{k=1}^{\infty} \frac {1}{n_k} is an irrational number. (N. 19)
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