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TOT 2006 Fall - Junior A-Level p6 1+1/2+1/3+...+1/n = a_n/b_n

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February 25, 2020
number theoryDecreasingSequence

Problem Statement

Let 1+1/2+1/3+...+1/n=an/bn1 + 1/2 + 1/3 +... + 1/n = a_n/b_n, where ana_n and bnb_n are relatively prime. Show that there exist infinitely many positive integers nn, such that bn+1<bnb_{n+1} < b_n. (8)
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